lst:=[[(d*x+c)^3*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,2,1/4*(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(d*x+c)^4/d^6-1/5*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))*(d*x+c)^5/d^6+1/6*(a*d^2*(C*d-3*D*c)+b*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*(d*x+c)^6/d^6+1/7*(a*d^2*D-b*(-B*d^2+4*C*c*d-10*D*c^2))*(d*x+c)^7/d^6+1/8*b*(C*d-5*D*c)*(d*x+c)^8/d^6+1/9*b*D*(d*x+c)^9/d^6,1],
[(d*x+c)^2*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,2,a*A*c^2*x+1/3*(a*c*(2*B*d+C*c)+A*(a*d^2+b*c^2))*x^3+1/4*a*(B*d^2+2*C*c*d+D*c^2)*x^4+1/5*(b*(A*d^2+2*B*c*d+C*c^2)+a*d*(C*d+2*D*c))*x^5+1/6*(a*d^2*D+b*(B*d^2+2*C*c*d+D*c^2))*x^6+1/7*b*d*(C*d+2*D*c)*x^7+1/8*b*d^2*D*x^8+1/4*c*(2*A*d+B*c)*(b*x^2+a)^2/b,1],
[(d*x+c)*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,2,a*A*c*x+1/2*a*(A*d+B*c)*x^2+1/3*(A*b*c+B*a*d+C*a*c)*x^3+1/4*(A*b*d+B*b*c+C*a*d+D*a*c)*x^4+1/5*(B*b*d+C*b*c+D*a*d)*x^5+1/6*b*(C*d+D*c)*x^6+1/7*b*d*D*x^7,1],
[(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,2,a*A*x+1/2*a*B*x^2+1/3*(A*b+C*a)*x^3+1/4*(B*b+D*a)*x^4+1/5*b*C*x^5+1/6*b*D*x^6,1],
[(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c),x,2,-(a*d^2*(-B*d^2+C*c*d-D*c^2)+b*c*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x/d^5+1/2*(a*d^2*(C*d-D*c)+b*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x^2/d^4+1/3*(a*d^2*D-b*(-B*d^2+C*c*d-D*c^2))*x^3/d^3+1/4*b*(C*d-D*c)*x^4/d^2+1/5*b*D*x^5/d+(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(d*x+c)/d^6,1],
[(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^2,x,2,(a*d^2*(C*d-2*D*c)+b*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x/d^5+1/2*(a*d^2*D-b*(-B*d^2+2*C*c*d-3*D*c^2))*x^2/d^4+1/3*b*(C*d-2*D*c)*x^3/d^3+1/4*b*D*x^4/d^2-(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/d^6/(d*x+c)-(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))*ln(d*x+c)/d^6,1],
[(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^3,x,2,(a*d^2*D-b*(-B*d^2+3*C*c*d-6*D*c^2))*x/d^5+1/2*b*(C*d-3*D*c)*x^2/d^4+1/3*b*D*x^3/d^3-1/2*(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/d^6/(d*x+c)^2+(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))/d^6/(d*x+c)+(a*d^2*(C*d-3*D*c)+b*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*ln(d*x+c)/d^6,1],
[(d*x+c)^3*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x,2,1/4*(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(d*x+c)^4/d^8-1/5*(a*d^2+b*c^2)*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(4*A*d^3-5*B*c*d^2+6*C*c^2*d-7*D*c^3))*(d*x+c)^5/d^8+1/6*(a^2*d^4*(C*d-3*D*c)+b^2*c^2*(6*A*d^3-10*B*c*d^2+15*C*c^2*d-21*D*c^3)+2*a*b*d^2*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*(d*x+c)^6/d^8+1/7*(a^2*d^4*D-2*a*b*d^2*(-B*d^2+4*C*c*d-10*D*c^2)-b^2*c*(4*A*d^3-10*B*c*d^2+20*C*c^2*d-35*D*c^3))*(d*x+c)^7/d^8+1/8*b*(2*a*d^2*(C*d-5*D*c)+b*(A*d^3-5*B*c*d^2+15*C*c^2*d-35*D*c^3))*(d*x+c)^8/d^8+1/9*b*(2*a*d^2*D-b*(-B*d^2+6*C*c*d-21*D*c^2))*(d*x+c)^9/d^8+1/10*b^2*(C*d-7*D*c)*(d*x+c)^10/d^8+1/11*b^2*D*(d*x+c)^11/d^8,1],
[(d*x+c)^2*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x,2,a^2*A*c^2*x+1/3*a*(a*c*(2*B*d+C*c)+A*(a*d^2+2*b*c^2))*x^3+1/4*a^2*(B*d^2+2*C*c*d+D*c^2)*x^4+1/5*(A*b*(2*a*d^2+b*c^2)+a*(2*b*c*(2*B*d+C*c)+a*d*(C*d+2*D*c)))*x^5+1/6*a*(a*d^2*D+2*b*(B*d^2+2*C*c*d+D*c^2))*x^6+1/7*b*(b*(A*d^2+2*B*c*d+C*c^2)+2*a*d*(C*d+2*D*c))*x^7+1/8*b*(2*a*d^2*D+b*(B*d^2+2*C*c*d+D*c^2))*x^8+1/9*b^2*d*(C*d+2*D*c)*x^9+1/10*b^2*d^2*D*x^10+1/6*c*(2*A*d+B*c)*(b*x^2+a)^3/b,1],
[(d*x+c)*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x,6,a^2*A*c*x+1/3*a*(2*A*b*c+B*a*d+C*a*c)*x^3+1/5*(A*b^2*c+a*(2*b*(B*d+C*c)+a*d*D))*x^5+1/7*b*(B*b*d+C*b*c+2*D*a*d)*x^7+1/9*b^2*d*D*x^9+1/6*(A*b*d+B*b*c-C*a*d-D*a*c)*(b*x^2+a)^3/b^2+1/8*(C*d+D*c)*(b*x^2+a)^4/b^2,1],
[(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x,2,a^2*A*x+1/3*a*(2*A*b+C*a)*x^3+1/4*a^2*D*x^4+1/5*b*(A*b+2*C*a)*x^5+1/3*a*b*D*x^6+1/7*b^2*C*x^7+1/8*b^2*D*x^8+1/6*B*(b*x^2+a)^3/b,1],
[(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c),x,2,-(a^2*d^4*(-B*d^2+C*c*d-D*c^2)+b^2*c^3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+2*a*b*c*d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x/d^7+1/2*(a^2*d^4*(C*d-D*c)+b^2*c^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+2*a*b*d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x^2/d^6+1/3*(a^2*d^4*D-2*a*b*d^2*(-B*d^2+C*c*d-D*c^2)-b^2*c*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x^3/d^5+1/4*b*(2*a*d^2*(C*d-D*c)+b*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x^4/d^4+1/5*b*(2*a*d^2*D-b*(-B*d^2+C*c*d-D*c^2))*x^5/d^3+1/6*b^2*(C*d-D*c)*x^6/d^2+1/7*b^2*D*x^7/d+(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(d*x+c)/d^8,1],
[(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^2,x,2,(a^2*d^4*(C*d-2*D*c)+b^2*c^2*(3*A*d^3-4*B*c*d^2+5*C*c^2*d-6*D*c^3)+2*a*b*d^2*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x/d^7+1/2*(a^2*d^4*D-2*a*b*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b^2*c*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))*x^2/d^6+1/3*b*(2*a*d^2*(C*d-2*D*c)+b*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x^3/d^5+1/4*b*(2*a*d^2*D-b*(-B*d^2+2*C*c*d-3*D*c^2))*x^4/d^4+1/5*b^2*(C*d-2*D*c)*x^5/d^3+1/6*b^2*D*x^6/d^2-(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/d^8/(d*x+c)-(a*d^2+b*c^2)*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(4*A*d^3-5*B*c*d^2+6*C*c^2*d-7*D*c^3))*ln(d*x+c)/d^8,1],
[(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^3,x,2,(a^2*d^4*D-2*a*b*d^2*(-B*d^2+3*C*c*d-6*D*c^2)-b^2*c*(3*A*d^3-6*B*c*d^2+10*C*c^2*d-15*D*c^3))*x/d^7+1/2*b*(2*a*d^2*(C*d-3*D*c)+b*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*x^2/d^6+1/3*b*(2*a*d^2*D-b*(-B*d^2+3*C*c*d-6*D*c^2))*x^3/d^5+1/4*b^2*(C*d-3*D*c)*x^4/d^4+1/5*b^2*D*x^5/d^3-1/2*(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/d^8/(d*x+c)^2+(a*d^2+b*c^2)*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(4*A*d^3-5*B*c*d^2+6*C*c^2*d-7*D*c^3))/d^8/(d*x+c)+(a^2*d^4*(C*d-3*D*c)+b^2*c^2*(6*A*d^3-10*B*c*d^2+15*C*c^2*d-21*D*c^3)+2*a*b*d^2*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*ln(d*x+c)/d^8,1],
[(d*x+c)^3*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x,2,1/4*(a*d^2+b*c^2)^3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(d*x+c)^4/d^10-1/5*(a*d^2+b*c^2)^2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(6*A*d^3-7*B*c*d^2+8*C*c^2*d-9*D*c^3))*(d*x+c)^5/d^10+1/6*(a*d^2+b*c^2)*(a^2*d^4*(C*d-3*D*c)+b^2*c^2*(15*A*d^3-21*B*c*d^2+28*C*c^2*d-36*D*c^3)+a*b*d^2*(3*A*d^3-9*B*c*d^2+17*C*c^2*d-27*D*c^3))*(d*x+c)^6/d^10+1/7*(a^3*d^6*D-3*a^2*b*d^4*(-B*d^2+4*C*c*d-10*D*c^2)-b^3*c^3*(20*A*d^3-35*B*c*d^2+56*C*c^2*d-84*D*c^3)-3*a*b^2*c*d^2*(4*A*d^3-10*B*c*d^2+20*C*c^2*d-35*D*c^3))*(d*x+c)^7/d^10+1/8*b*(3*a^2*d^4*(C*d-5*D*c)+b^2*c^2*(15*A*d^3-35*B*c*d^2+70*C*c^2*d-126*D*c^3)+3*a*b*d^2*(A*d^3-5*B*c*d^2+15*C*c^2*d-35*D*c^3))*(d*x+c)^8/d^10+1/9*b*(3*a^2*d^4*D-3*a*b*d^2*(-B*d^2+6*C*c*d-21*D*c^2)-b^2*c*(6*A*d^3-21*B*c*d^2+56*C*c^2*d-126*D*c^3))*(d*x+c)^9/d^10+1/10*b^2*(3*a*d^2*(C*d-7*D*c)+b*(A*d^3-7*B*c*d^2+28*C*c^2*d-84*D*c^3))*(d*x+c)^10/d^10+1/11*b^2*(3*a*d^2*D-b*(-B*d^2+8*C*c*d-36*D*c^2))*(d*x+c)^11/d^10+1/12*b^3*(C*d-9*D*c)*(d*x+c)^12/d^10+1/13*b^3*D*(d*x+c)^13/d^10,1],
[(d*x+c)^2*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x,2,a^3*A*c^2*x+1/2*a^3*c*(2*A*d+B*c)*x^2+1/3*a^2*(a*c*(2*B*d+C*c)+A*(a*d^2+3*b*c^2))*x^3+1/4*a^2*(3*b*c*(2*A*d+B*c)+a*(B*d^2+2*C*c*d+D*c^2))*x^4+1/5*a*(3*A*b*(a*d^2+b*c^2)+a*(3*b*c*(2*B*d+C*c)+a*d*(C*d+2*D*c)))*x^5+1/6*a*(3*b^2*c*(2*A*d+B*c)+a^2*d^2*D+3*a*b*(B*d^2+2*C*c*d+D*c^2))*x^6+1/7*b*(A*b*(3*a*d^2+b*c^2)+3*a*(b*c*(2*B*d+C*c)+a*d*(C*d+2*D*c)))*x^7+1/8*b*(b^2*c*(2*A*d+B*c)+3*a^2*d^2*D+3*a*b*(B*d^2+2*C*c*d+D*c^2))*x^8+1/9*b^2*(b*(A*d^2+2*B*c*d+C*c^2)+3*a*d*(C*d+2*D*c))*x^9+1/10*b^2*(3*a*d^2*D+b*(B*d^2+2*C*c*d+D*c^2))*x^10+1/11*b^3*d*(C*d+2*D*c)*x^11+1/12*b^3*d^2*D*x^12,1],
[(d*x+c)*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x,6,a^3*A*c*x+1/3*a^2*(3*A*b*c+B*a*d+C*a*c)*x^3+1/5*a*(3*A*b^2*c+a*(3*b*(B*d+C*c)+a*d*D))*x^5+1/7*b*(A*b^2*c+3*a*(B*b*d+C*b*c+D*a*d))*x^7+1/9*b^2*(B*b*d+C*b*c+3*D*a*d)*x^9+1/11*b^3*d*D*x^11+1/8*(A*b*d+B*b*c-C*a*d-D*a*c)*(b*x^2+a)^4/b^2+1/10*(C*d+D*c)*(b*x^2+a)^5/b^2,1],
[(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x,2,a^3*A*x+1/3*a^2*(3*A*b+C*a)*x^3+1/4*a^3*D*x^4+3/5*a*b*(A*b+C*a)*x^5+1/2*a^2*b*D*x^6+1/7*b^2*(A*b+3*C*a)*x^7+3/8*a*b^2*D*x^8+1/9*b^3*C*x^9+1/10*b^3*D*x^10+1/8*B*(b*x^2+a)^4/b,1],
[(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c),x,2,-(a*d^2+b*c^2)^2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(6*A*d^3-7*B*c*d^2+8*C*c^2*d-9*D*c^3))*x/d^9+1/2*(a*d^2+b*c^2)*(a^2*d^4*(C*d-3*D*c)+b^2*c^2*(15*A*d^3-21*B*c*d^2+28*C*c^2*d-36*D*c^3)+a*b*d^2*(3*A*d^3-9*B*c*d^2+17*C*c^2*d-27*D*c^3))*(d*x+c)^2/d^10+1/3*(a^3*d^6*D-3*a^2*b*d^4*(-B*d^2+4*C*c*d-10*D*c^2)-b^3*c^3*(20*A*d^3-35*B*c*d^2+56*C*c^2*d-84*D*c^3)-3*a*b^2*c*d^2*(4*A*d^3-10*B*c*d^2+20*C*c^2*d-35*D*c^3))*(d*x+c)^3/d^10+1/4*b*(3*a^2*d^4*(C*d-5*D*c)+b^2*c^2*(15*A*d^3-35*B*c*d^2+70*C*c^2*d-126*D*c^3)+3*a*b*d^2*(A*d^3-5*B*c*d^2+15*C*c^2*d-35*D*c^3))*(d*x+c)^4/d^10+1/5*b*(3*a^2*d^4*D-3*a*b*d^2*(-B*d^2+6*C*c*d-21*D*c^2)-b^2*c*(6*A*d^3-21*B*c*d^2+56*C*c^2*d-126*D*c^3))*(d*x+c)^5/d^10+1/6*b^2*(3*a*d^2*(C*d-7*D*c)+b*(A*d^3-7*B*c*d^2+28*C*c^2*d-84*D*c^3))*(d*x+c)^6/d^10+1/7*b^2*(3*a*d^2*D-b*(-B*d^2+8*C*c*d-36*D*c^2))*(d*x+c)^7/d^10+1/8*b^3*(C*d-9*D*c)*(d*x+c)^8/d^10+1/9*b^3*D*(d*x+c)^9/d^10+(a*d^2+b*c^2)^3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(d*x+c)/d^10,1],
[(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^2,x,2,(a^3*d^6*(C*d-2*D*c)+b^3*c^4*(5*A*d^3-6*B*c*d^2+7*C*c^2*d-8*D*c^3)+3*a*b^2*c^2*d^2*(3*A*d^3-4*B*c*d^2+5*C*c^2*d-6*D*c^3)+3*a^2*b*d^4*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x/d^9+1/2*(a^3*d^6*D-3*a^2*b*d^4*(-B*d^2+2*C*c*d-3*D*c^2)-b^3*c^3*(4*A*d^3-5*B*c*d^2+6*C*c^2*d-7*D*c^3)-3*a*b^2*c*d^2*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))*x^2/d^8+1/3*b*(3*a^2*d^4*(C*d-2*D*c)+b^2*c^2*(3*A*d^3-4*B*c*d^2+5*C*c^2*d-6*D*c^3)+3*a*b*d^2*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x^3/d^7+1/4*b*(3*a^2*d^4*D-3*a*b*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b^2*c*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))*x^4/d^6+1/5*b^2*(3*a*d^2*(C*d-2*D*c)+b*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x^5/d^5+1/6*b^2*(3*a*d^2*D-b*(-B*d^2+2*C*c*d-3*D*c^2))*x^6/d^4+1/7*b^3*(C*d-2*D*c)*x^7/d^3+1/8*b^3*D*x^8/d^2-(a*d^2+b*c^2)^3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/d^10/(d*x+c)-(a*d^2+b*c^2)^2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(6*A*d^3-7*B*c*d^2+8*C*c^2*d-9*D*c^3))*ln(d*x+c)/d^10,1],
[(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^3,x,2,(a^3*d^6*D-3*a^2*b*d^4*(-B*d^2+3*C*c*d-6*D*c^2)-b^3*c^3*(10*A*d^3-15*B*c*d^2+21*C*c^2*d-28*D*c^3)-3*a*b^2*c*d^2*(3*A*d^3-6*B*c*d^2+10*C*c^2*d-15*D*c^3))*x/d^9+1/2*b*(3*a^2*d^4*(C*d-3*D*c)+b^2*c^2*(6*A*d^3-10*B*c*d^2+15*C*c^2*d-21*D*c^3)+3*a*b*d^2*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*x^2/d^8+1/3*b*(3*a^2*d^4*D-3*a*b*d^2*(-B*d^2+3*C*c*d-6*D*c^2)-b^2*c*(3*A*d^3-6*B*c*d^2+10*C*c^2*d-15*D*c^3))*x^3/d^7+1/4*b^2*(3*a*d^2*(C*d-3*D*c)+b*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*x^4/d^6+1/5*b^2*(3*a*d^2*D-b*(-B*d^2+3*C*c*d-6*D*c^2))*x^5/d^5+1/6*b^3*(C*d-3*D*c)*x^6/d^4+1/7*b^3*D*x^7/d^3-1/2*(a*d^2+b*c^2)^3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/d^10/(d*x+c)^2+(a*d^2+b*c^2)^2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(6*A*d^3-7*B*c*d^2+8*C*c^2*d-9*D*c^3))/d^10/(d*x+c)+(a*d^2+b*c^2)*(a^2*d^4*(C*d-3*D*c)+b^2*c^2*(15*A*d^3-21*B*c*d^2+28*C*c^2*d-36*D*c^3)+a*b*d^2*(3*A*d^3-9*B*c*d^2+17*C*c^2*d-27*D*c^3))*ln(d*x+c)/d^10,1],
[(b*x^2+a)*(3*b*c*x^2+4*b^2*x-a*c)/(c*x+b)^2,x,1,(b*x^2+a)^2/(c*x+b),1],
[(b*x^2+a)*(-a*c+b*x*(3*c*x+4*b))/(c*x+b)^2,x,1,(b*x^2+a)^2/(c*x+b),1],
[(b*x^2+a)^2*(5*b*c*x^2+6*b^2*x-a*c)/(c*x+b)^2,x,1,(b*x^2+a)^3/(c*x+b),1],
[(b*x^2+a)^2*(-a*c+b*x*(5*c*x+6*b))/(c*x+b)^2,x,1,(b*x^2+a)^3/(c*x+b),1],
[(d*x+c)^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x,5,(b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+a^2*d^3*D-a*b*d*(B*d^2+3*C*c*d+3*D*c^2))*x/b^3-1/2*(a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*x^2/b^2-1/3*d*(a*d^2*D-b*(B*d^2+3*C*c*d+3*D*c^2))*x^3/b^2+1/4*d^2*(C*d+3*D*c)*x^4/b+1/5*d^3*D*x^5/b+(A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(3*B*d+C*c)+a^2*d^3*D-a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(7/2)+1/2*(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*ln(b*x^2+a)/b^3,1],
[(d*x+c)^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x,5,(b*(A*d^2+2*B*c*d+C*c^2)-a*d*(C*d+2*D*c))*x/b^2-1/2*(a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))*x^2/b^2+1/3*d*(C*d+2*D*c)*x^3/b+1/4*d^2*D*x^4/b+(A*b*(-a*d^2+b*c^2)-a*(b*c*(2*B*d+C*c)-a*d*(C*d+2*D*c)))*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(5/2)+1/2*(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))*ln(b*x^2+a)/b^3,1],
[(d*x+c)*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x,5,(B*b*d+C*b*c-D*a*d)*x/b^2+1/2*(C*d+D*c)*x^2/b+1/3*d*D*x^3/b+(A*b^2*c-a*(b*(B*d+C*c)-a*d*D))*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(5/2)+1/2*(A*b*d+B*b*c-C*a*d-D*a*c)*ln(b*x^2+a)/b^2,1],
[(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x,5,C*x/b+1/2*D*x^2/b+(A*b-C*a)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(3/2)+1/2*(B*b-D*a)*ln(b*x^2+a)/b^2,1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)/(b*x^2+a),x,5,D*x/b/d+(A*b^2*c-a*(-B*b*d+C*b*c+D*a*d))*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(3/2)/(a*d^2+b*c^2)+(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(d*x+c)/d^2/(a*d^2+b*c^2)+1/2*(-A*b*d+B*b*c+C*a*d-D*a*c)*ln(b*x^2+a)/b/(a*d^2+b*c^2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^2/(b*x^2+a),x,5,-(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/d^2/(a*d^2+b*c^2)/(d*x+c)+(A*b*(-a*d^2+b*c^2)-a*(b*c*(-2*B*d+C*c)-a*d*(C*d-2*D*c)))*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/sqrt(b)/(a*d^2+b*c^2)^2-(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-2*A*d^3+B*c*d^2-D*c^3))*ln(d*x+c)/d^2/(a*d^2+b*c^2)^2+1/2*(b^2*c*(-2*A*d+B*c)+a^2*d^2*D+a*b*(-B*d^2+2*C*c*d-D*c^2))*ln(b*x^2+a)/b/(a*d^2+b*c^2)^2,1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^3/(b*x^2+a),x,5,1/2*(-A*d^3+B*c*d^2-C*c^2*d+D*c^3)/d^2/(a*d^2+b*c^2)/(d*x+c)^2+(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-2*A*d^3+B*c*d^2-D*c^3))/d^2/(a*d^2+b*c^2)^2/(d*x+c)+(A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(-3*B*d+C*c)-a^2*d^3*D-a*b*d*(-B*d^2+3*C*c*d-3*D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/sqrt(b)/(a*d^2+b*c^2)^3-(b^2*c^2*(-3*A*d+B*c)-a^2*d^2*(C*d-3*D*c)+a*b*(A*d^3-3*B*c*d^2+3*C*c^2*d-D*c^3))*ln(d*x+c)/(a*d^2+b*c^2)^3+1/2*(b^2*c^2*(-3*A*d+B*c)-a^2*d^2*(C*d-3*D*c)+a*b*(A*d^3-3*B*c*d^2+3*C*c^2*d-D*c^3))*ln(b*x^2+a)/(a*d^2+b*c^2)^3,1],
[(d*x+c)^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x,8,-d*(2*a*d^2*D-b*(B*d^2+3*C*c*d+3*D*c^2))*x/b^3+1/2*d^2*(C*d+3*D*c)*x^2/b^2+1/3*d^3*D*x^3/b^2-1/2*(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))/b^3/(b*x^2+a)+1/2*(A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(3*B*d+C*c)+a^2*d^3*D-a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x/a/b^3/(b*x^2+a)+1/2*(A*b^2*c*(3*a*d^2+b*c^2)+a*(b^2*c^2*(3*B*d+C*c)+5*a^2*d^3*D-3*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(7/2)-1/2*(2*a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*ln(b*x^2+a)/b^3,1],
[(d*x+c)^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x,7,d*(C*d+2*D*c)*x/b^2+1/2*d^2*D*x^2/b^2-1/2*(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))/b^3/(b*x^2+a)+1/2*(A*b*(-a*d^2+b*c^2)-a*(b*c*(2*B*d+C*c)-a*d*(C*d+2*D*c)))*x/a/b^2/(b*x^2+a)+1/2*(A*b*(a*d^2+b*c^2)+a*(b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(5/2)-1/2*(2*a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))*ln(b*x^2+a)/b^3,1],
[(d*x+c)*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x,7,d*D*x/b^2-1/2*(A*b*d+B*b*c-C*a*d-D*a*c)/b^2/(b*x^2+a)+1/2*(A*b^2*c-a*(b*(B*d+C*c)-a*d*D))*x/a/b^2/(b*x^2+a)+1/2*(A*b^2*c+a*(B*b*d+C*b*c-3*D*a*d))*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(5/2)+1/2*(C*d+D*c)*ln(b*x^2+a)/b^2,1],
[(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x,6,-1/2*(B*b-D*a)/b^2/(b*x^2+a)+1/2*(A*b-C*a)*x/a/b/(b*x^2+a)+1/2*(A*b+C*a)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(3/2)+1/2*D*ln(b*x^2+a)/b^2,1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)/(b*x^2+a)^2,x,6,-1/2*(a*(-A*b*d+B*b*c+C*a*d-D*a*c)-(A*b^2*c-a*(-B*b*d+C*b*c+D*a*d))*x)/a/b/(a*d^2+b*c^2)/(b*x^2+a)+1/2*(A*b^2*c*(3*a*d^2+b*c^2)+a*(b^2*c^2*(-B*d+C*c)+a^2*d^3*D-a*b*d*(-B*d^2+C*c*d-3*D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(3/2)/(a*d^2+b*c^2)^2+(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(d*x+c)/(a*d^2+b*c^2)^2-1/2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(b*x^2+a)/(a*d^2+b*c^2)^2,1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^2/(b*x^2+a)^2,x,6,-(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/(a*d^2+b*c^2)^2/(d*x+c)-1/2*(a*(b^2*c*(-2*A*d+B*c)+a^2*d^2*D+a*b*(-B*d^2+2*C*c*d-D*c^2))-b*(A*b*(-a*d^2+b*c^2)-a*(b*c*(-2*B*d+C*c)-a*d*(C*d-2*D*c)))*x)/a/b/(a*d^2+b*c^2)^2/(b*x^2+a)+1/2*(A*b*(-3*a^2*d^4+6*a*b*c^2*d^2+b^2*c^4)+a*(b^2*c^3*(-2*B*d+C*c)+a^2*d^3*(C*d-2*D*c)-6*a*b*c*d*(-B*d^2+C*c*d-D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/sqrt(b)/(a*d^2+b*c^2)^3-(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(4*A*d^3-3*B*c*d^2+2*C*c^2*d-D*c^3))*ln(d*x+c)/(a*d^2+b*c^2)^3+1/2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(4*A*d^3-3*B*c*d^2+2*C*c^2*d-D*c^3))*ln(b*x^2+a)/(a*d^2+b*c^2)^3,1],
[(d*x+c)^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x,8,d^3*D*x/b^3-1/4*(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))/b^3/(b*x^2+a)^2+1/4*(A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(3*B*d+C*c)+a^2*d^3*D-a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x/a/b^3/(b*x^2+a)^2+1/2*(2*a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))/b^3/(b*x^2+a)+1/8*(3*A*b^2*c*(a*d^2+b*c^2)+a*(b^2*c^2*(3*B*d+C*c)+9*a^2*d^3*D-5*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x/a^2/b^3/(b*x^2+a)+1/8*(3*A*b^2*c*(a*d^2+b*c^2)+a*(b^2*c^2*(3*B*d+C*c)-15*a^2*d^3*D+3*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(7/2)+1/2*d^2*(C*d+3*D*c)*ln(b*x^2+a)/b^3,1],
[(d*x+c)^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x,7,-1/4*(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))/b^3/(b*x^2+a)^2+1/4*(A*b*(-a*d^2+b*c^2)-a*(b*c*(2*B*d+C*c)-a*d*(C*d+2*D*c)))*x/a/b^2/(b*x^2+a)^2+1/2*(2*a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))/b^3/(b*x^2+a)+1/8*(A*b*(a*d^2+3*b*c^2)+a*(b*c*(2*B*d+C*c)-5*a*d*(C*d+2*D*c)))*x/a^2/b^2/(b*x^2+a)+1/8*(A*b*(a*d^2+3*b*c^2)+a*(b*c*(2*B*d+C*c)+3*a*d*(C*d+2*D*c)))*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(5/2)+1/2*d^2*D*ln(b*x^2+a)/b^3,1],
[(d*x+c)*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x,6,1/4*(A*b^2*c-a*(b*(B*d+C*c)-a*d*D))*x/a/b^2/(b*x^2+a)^2+1/8*(3*A*b^2*c+a*(B*b*d+C*b*c-5*D*a*d))*x/a^2/b^2/(b*x^2+a)-1/4*(B*c+A*d+(C*d+D*c)*x^2)^2/(A*b*d+B*b*c-C*a*d-D*a*c)/(b*x^2+a)^2+1/8*(3*A*b^2*c+a*(B*b*d+C*b*c+3*D*a*d))*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(5/2),1],
[(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x,6,1/4*(A*b-C*a)*x/a/b/(b*x^2+a)^2+1/8*(3*A*b+C*a)*x/a^2/b/(b*x^2+a)-1/4*(D*x^2+B)^2/(B*b-D*a)/(b*x^2+a)^2+1/8*(3*A*b+C*a)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(3/2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)/(b*x^2+a)^3,x,7,-1/4*(a*(-A*b*d+B*b*c+C*a*d-D*a*c)-(A*b^2*c-a*(-B*b*d+C*b*c+D*a*d))*x)/a/b/(a*d^2+b*c^2)/(b*x^2+a)^2+1/8*(4*a^2*b*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+(A*b^2*c*(7*a*d^2+3*b*c^2)+a*(b^2*c^2*(-B*d+C*c)+a^2*d^3*D-a*b*d*(-3*B*d^2+3*C*c*d-5*D*c^2)))*x)/a^2/b/(a*d^2+b*c^2)^2/(b*x^2+a)+1/8*(A*b^2*c*(15*a^2*d^4+10*a*b*c^2*d^2+3*b^2*c^4)+a*(b^3*c^4*(-B*d+C*c)+a^3*d^5*D-3*a^2*b*d^3*(-B*d^2+C*c*d-2*D*c^2)+3*a*b^2*c^2*d*(-2*B*d^2+2*C*c*d-D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(3/2)/(a*d^2+b*c^2)^3+d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(d*x+c)/(a*d^2+b*c^2)^3-1/2*d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(b*x^2+a)/(a*d^2+b*c^2)^3,1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^2/(b*x^2+a)^3,x,7,-d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)/(a*d^2+b*c^2)^3/(d*x+c)-1/4*(a*(b^2*c*(-2*A*d+B*c)+a^2*d^2*D+a*b*(-B*d^2+2*C*c*d-D*c^2))-b*(A*b*(-a*d^2+b*c^2)-a*(b*c*(-2*B*d+C*c)-a*d*(C*d-2*D*c)))*x)/a/b/(a*d^2+b*c^2)^2/(b*x^2+a)^2-1/8*(4*a^2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(4*A*d^3-3*B*c*d^2+2*C*c^2*d-D*c^3))-(A*b*(-7*a^2*d^4+12*a*b*c^2*d^2+3*b^2*c^4)+a*(b^2*c^3*(-2*B*d+C*c)+3*a^2*d^3*(C*d-2*D*c)-2*a*b*c*d*(-7*B*d^2+6*C*c*d-5*D*c^2)))*x)/a^2/(a*d^2+b*c^2)^3/(b*x^2+a)+1/8*(3*A*b*(-5*a^3*d^6+15*a^2*b*c^2*d^4+5*a*b^2*c^4*d^2+b^3*c^6)+a*(b^3*c^5*(-2*B*d+C*c)+3*a^3*d^5*(C*d-2*D*c)-3*a^2*b*c*d^3*(-10*B*d^2+11*C*c*d-12*D*c^2)+a*b^2*c^3*d*(-20*B*d^2+13*C*c*d-6*D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/sqrt(b)/(a*d^2+b*c^2)^4-d^2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(6*A*d^3-5*B*c*d^2+4*C*c^2*d-3*D*c^3))*ln(d*x+c)/(a*d^2+b*c^2)^4+1/2*d^2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(6*A*d^3-5*B*c*d^2+4*C*c^2*d-3*D*c^3))*ln(b*x^2+a)/(a*d^2+b*c^2)^4,1],
[(d*x+c)^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^4,x,8,-1/6*(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))/b^3/(b*x^2+a)^3+1/6*(A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(3*B*d+C*c)+a^2*d^3*D-a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x/a/b^3/(b*x^2+a)^3+1/4*(2*a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))/b^3/(b*x^2+a)^2+1/24*(A*b^2*c*(3*a*d^2+5*b*c^2)+a*(b^2*c^2*(3*B*d+C*c)+13*a^2*d^3*D-7*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x/a^2/b^3/(b*x^2+a)^2-1/2*d^2*(C*d+3*D*c)/b^3/(b*x^2+a)+1/16*(A*b^2*c*(3*a*d^2+5*b*c^2)+a*(b^2*c^2*(3*B*d+C*c)-11*a^2*d^3*D+a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x/a^3/b^3/(b*x^2+a)+1/16*(A*b^2*c*(3*a*d^2+5*b*c^2)+a*(b^2*c^2*(3*B*d+C*c)+5*a^2*d^3*D+a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/a^(7/2)/b^(7/2),1],
[(d*x+c)^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^4,x,8,-1/6*(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))/b^3/(b*x^2+a)^3+1/6*(A*b*(-a*d^2+b*c^2)-a*(b*c*(2*B*d+C*c)-a*d*(C*d+2*D*c)))*x/a/b^2/(b*x^2+a)^3+1/4*(2*a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))/b^3/(b*x^2+a)^2+1/24*(A*b*(a*d^2+5*b*c^2)+a*(b*c*(2*B*d+C*c)-7*a*d*(C*d+2*D*c)))*x/a^2/b^2/(b*x^2+a)^2-1/2*d^2*D/b^3/(b*x^2+a)+1/16*(A*b*(a*d^2+5*b*c^2)+a*(b*c*(2*B*d+C*c)+a*d*(C*d+2*D*c)))*x/a^3/b^2/(b*x^2+a)+1/16*(A*b*(a*d^2+5*b*c^2)+a*(b*c*(2*B*d+C*c)+a*d*(C*d+2*D*c)))*arctan(sqrt(b)*x/sqrt(a))/a^(7/2)/b^(5/2),1],
[(d*x+c)*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^4,x,8,-1/6*(A*b*d+B*b*c-C*a*d-D*a*c)/b^2/(b*x^2+a)^3+1/6*(A*b^2*c-a*(b*(B*d+C*c)-a*d*D))*x/a/b^2/(b*x^2+a)^3-1/4*(C*d+D*c)/b^2/(b*x^2+a)^2+1/24*(5*A*b^2*c+a*(B*b*d+C*b*c-7*D*a*d))*x/a^2/b^2/(b*x^2+a)^2+1/16*(5*A*b^2*c+a*(B*b*d+C*b*c+D*a*d))*x/a^3/b^2/(b*x^2+a)+1/16*(5*A*b^2*c+a*(B*b*d+C*b*c+D*a*d))*arctan(sqrt(b)*x/sqrt(a))/a^(7/2)/b^(5/2),1],
[(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^4,x,8,-1/6*(B*b-D*a)/b^2/(b*x^2+a)^3+1/6*(A*b-C*a)*x/a/b/(b*x^2+a)^3-1/4*D/b^2/(b*x^2+a)^2+1/24*(5*A*b+C*a)*x/a^2/b/(b*x^2+a)^2+1/16*(5*A*b+C*a)*x/a^3/b/(b*x^2+a)+1/16*(5*A*b+C*a)*arctan(sqrt(b)*x/sqrt(a))/a^(7/2)/b^(3/2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)/(b*x^2+a)^4,x,8,-1/6*(a*(-A*b*d+B*b*c+C*a*d-D*a*c)-(A*b^2*c-a*(-B*b*d+C*b*c+D*a*d))*x)/a/b/(a*d^2+b*c^2)/(b*x^2+a)^3+1/24*(6*a^2*b*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+(A*b^2*c*(11*a*d^2+5*b*c^2)+a*(b^2*c^2*(-B*d+C*c)+a^2*d^3*D-a*b*d*(-5*B*d^2+5*C*c*d-7*D*c^2)))*x)/a^2/b/(a*d^2+b*c^2)^2/(b*x^2+a)^2+1/16*(8*a^3*b*d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+(A*b^2*c*(19*a^2*d^4+16*a*b*c^2*d^2+5*b^2*c^4)+a*(b^3*c^4*(-B*d+C*c)+a^3*d^5*D-a^2*b*d^3*(-5*B*d^2+5*C*c*d-8*D*c^2)+a*b^2*c^2*d*(-4*B*d^2+4*C*c*d-D*c^2)))*x)/a^3/b/(a*d^2+b*c^2)^3/(b*x^2+a)+1/16*(A*b^2*c*(35*a^3*d^6+35*a^2*b*c^2*d^4+21*a*b^2*c^4*d^2+5*b^3*c^6)+a*(b^4*c^6*(-B*d+C*c)+a^4*d^7*D-a^3*b*d^5*(-5*B*d^2+5*C*c*d-9*D*c^2)+3*a^2*b^2*c^2*d^3*(-5*B*d^2+5*C*c*d-3*D*c^2)+a*b^3*c^4*d*(-5*B*d^2+5*C*c*d-D*c^2)))*arctan(sqrt(b)*x/sqrt(a))/a^(7/2)/b^(3/2)/(a*d^2+b*c^2)^4+d^4*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(d*x+c)/(a*d^2+b*c^2)^4-1/2*d^4*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*ln(b*x^2+a)/(a*d^2+b*c^2)^4,1],
[x^3*(x^2+x+1)/(x^2+1)^2,x,7,3/2*x+1/2*x^2-x^3/(2*x^2+2)-3/2*arctan(x)-1/2*ln(x^2+1),1],
[x^2*(x^2+x+1)/(x^2+1)^2,x,6,x+1/(2*x^2+2)-arctan(x)+1/2*ln(x^2+1),1],
[x*(x^2+x+1)/(x^2+1)^2,x,4,-1/2*x/(x^2+1)+1/2*arctan(x)+1/2*ln(x^2+1),1],
[(x^2+x+1)/(x^2+1)^2,x,3,-1/2/(x^2+1)+arctan(x),1],
[(x^2+x+1)/x/(x^2+1)^2,x,7,x/(2*x^2+2)+1/2*arctan(x)+ln(x)-1/2*ln(x^2+1),1],
[(x^2+x+1)/x^2/(x^2+1)^2,x,6,-1/x+1/(2*x^2+2)-arctan(x)+ln(x)-1/2*ln(x^2+1),1],
[(x^2+x+1)/x^3/(x^2+1)^2,x,7,-1/2/x^2-3/2/x+1/2/x/(x^2+1)-3/2*arctan(x)-ln(x)+1/2*ln(x^2+1),1],
[(x^2+2*x+1)/(x^2+1)^2,x,3,-1/(x^2+1)+arctan(x),1],
[(3*x^2+12*x+2)/(x^2+4)^2,x,4,-6/(x^2+4)-5*x/(4*x^2+16)+7/8*arctan(1/2*x),1],
[(d*x+c)^3*sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,10,1/128*(64*A*b^3*c^3-a*(16*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-8*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x*sqrt(b*x^2+a)/b^3+1/3*(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*(b*x^2+a)^(3/2)/b^3+1/64*(16*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-8*a*b*d*(B*d^2+3*C*c*d+3*D*c^2))*x*(b*x^2+a)^(3/2)/b^3-1/48*d*(5*a*d^2*D-8*b*(B*d^2+3*C*c*d+3*D*c^2))*x^3*(b*x^2+a)^(3/2)/b^2+1/8*d^3*D*x^5*(b*x^2+a)^(3/2)/b-1/5*(2*a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*(b*x^2+a)^(5/2)/b^3+1/7*d^2*(C*d+3*D*c)*(b*x^2+a)^(7/2)/b^3+1/128*a*(64*A*b^3*c^3-a*(16*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-8*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x+c)^2*sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,9,1/16*(2*A*b*(-a*d^2+4*b*c^2)-a*(2*b*c*(2*B*d+C*c)-a*d*(C*d+2*D*c)))*x*sqrt(b*x^2+a)/b^2+1/3*(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))*(b*x^2+a)^(3/2)/b^3+1/8*(2*b*(A*d^2+2*B*c*d+C*c^2)-a*d*(C*d+2*D*c))*x*(b*x^2+a)^(3/2)/b^2+1/6*d*(C*d+2*D*c)*x^3*(b*x^2+a)^(3/2)/b-1/5*(2*a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))*(b*x^2+a)^(5/2)/b^3+1/7*d^2*D*(b*x^2+a)^(7/2)/b^3+1/16*a*(2*A*b*(-a*d^2+4*b*c^2)-a*(2*b*c*(2*B*d+C*c)-a*d*(C*d+2*D*c)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)*sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,9,1/16*(8*A*b^2*c-a*(2*b*(B*d+C*c)-a*d*D))*x*sqrt(b*x^2+a)/b^2+1/3*(A*b*d+B*b*c-C*a*d-D*a*c)*(b*x^2+a)^(3/2)/b^2+1/8*(2*b*(B*d+C*c)-a*d*D)*x*(b*x^2+a)^(3/2)/b^2+1/6*d*D*x^3*(b*x^2+a)^(3/2)/b+1/5*(C*d+D*c)*(b*x^2+a)^(5/2)/b^2+1/16*a*(8*A*b^2*c-a*(2*b*(B*d+C*c)-a*d*D))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,8,1/8*(4*A*b-C*a)*x*sqrt(b*x^2+a)/b+1/3*(B*b-D*a)*(b*x^2+a)^(3/2)/b^2+1/4*C*x*(b*x^2+a)^(3/2)/b+1/5*D*(b*x^2+a)^(5/2)/b^2+1/8*a*(4*A*b-C*a)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c),x,9,(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^4-1/8*(a*d^2*D+4*b*(-B*d^2+C*c*d-D*c^2))*x*sqrt(b*x^2+a)/b/d^3+1/12*(4*C*d-7*D*c)*(b*x^2+a)^(3/2)/b/d^2+1/4*D*(d*x+c)*(b*x^2+a)^(3/2)/b/d^2-1/8*(a^2*d^4*D+4*a*b*d^2*(-B*d^2+C*c*d-D*c^2)+8*b^2*c*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/d^5-sqrt(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^5,1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^2,x,9,1/3*(a*d^2*D-3*b*(-B*d^2+2*C*c*d-3*D*c^2))*sqrt(b*x^2+a)/b/d^4+1/2*(C*d-2*D*c)*x*sqrt(b*x^2+a)/d^3+1/3*D*x^2*sqrt(b*x^2+a)/d^2-(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^4/(d*x+c)+1/2*(a*d^2*(C*d-2*D*c)+b*(2*A*d^3-4*B*c*d^2+6*C*c^2*d-8*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/d^5+(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^5/sqrt(a*d^2+b*c^2),1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^3,x,9,(C*d-3*D*c)*sqrt(b*x^2+a)/d^4+1/2*D*x*sqrt(b*x^2+a)/d^3-1/2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^4/(d*x+c)^2+1/2*(2*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(A*d^3-3*B*c*d^2+5*C*c^2*d-7*D*c^3))*sqrt(b*x^2+a)/d^4/(a*d^2+b*c^2)/(d*x+c)+1/2*(a*d^2*D-2*b*(-B*d^2+3*C*c*d-6*D*c^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/d^5-1/2*(2*a^2*d^4*(C*d-3*D*c)+2*b^2*c^3*(-B*d^2+3*C*c*d-6*D*c^2)+a*b*d^2*(A*d^3-3*B*c*d^2+9*C*c^2*d-19*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^5/(a*d^2+b*c^2)^(3/2),1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^4,x,9,D*sqrt(b*x^2+a)/d^4+1/2*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*(-A*c*d^3+C*c^3*d-2*D*c^4))*sqrt(b*x^2+a)/d^4/(a*d^2+b*c^2)/(d*x+c)^2-1/2*(2*a^2*d^4*(C*d-3*D*c)+a*b*c*d^2*(-B*d^2+6*C*c*d-15*D*c^2)+b^2*(-A*c^2*d^3+3*C*c^4*d-8*D*c^5))*sqrt(b*x^2+a)/d^4/(a*d^2+b*c^2)^2/(d*x+c)-1/3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^3+sqrt(b)*(C*d-4*D*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^5-1/2*(2*a^3*d^6*D-2*b^3*c^5*(C*d-4*D*c)-a^2*b*d^4*(-B*d^2+4*C*c*d-15*D*c^2)-a*b^2*c*d^2*(-A*d^3+5*C*c^2*d-20*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^5/(a*d^2+b*c^2)^(5/2),1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^5,x,8,-1/8*(8*b^3*c^7*D+4*a^3*d^6*(C*d-D*c)-a^2*b*d^4*(A*d^3-5*B*c*d^2+C*c^2*d-13*D*c^3)+4*a*b^2*c^2*d^2*(A*d^3+5*D*c^3)-d*(A*b^2*c*d^3*(-a*d^2+4*b*c^2)-12*b^3*c^6*D-8*a^3*d^6*D+4*a^2*b*c*d^4*(C*d-9*D*c)-a*b^2*c^2*d^2*(-5*B*d^2+C*c*d+35*D*c^2))*x)*sqrt(b*x^2+a)/d^4/(a*d^2+b*c^2)^3/(d*x+c)^2-1/4*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^4+1/12*(4*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-5*A*d^3+B*c*d^2+3*C*c^2*d-7*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^3+sqrt(b)*D*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^5+1/8*b*(8*b^3*c^7*D-4*a^3*d^6*(C*d-5*D*c)-4*a*b^2*c^2*d^2*(A*d^3-7*D*c^3)+a^2*b*d^4*(A*d^3-5*B*c*d^2+C*c^2*d+35*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^5/(a*d^2+b*c^2)^(7/2),1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^6,x,6,-1/8*(A*b^2*c*(-3*a*d^2+4*b*c^2)-a*(b^2*c^2*(-6*B*d+C*c)-4*a^2*d^3*D-a*b*d*(-B*d^2+6*C*c*d-3*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^4/(d*x+c)^2-1/5*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^5+1/20*(5*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-7*A*d^3+2*B*c*d^2+3*C*c^2*d-8*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^4-1/60*(20*a^2*d^4*(C*d-3*D*c)-b^2*c^2*(-27*A*d^3+2*B*c*d^2+3*C*c^2*d+12*D*c^3)-a*b*d^2*(8*A*d^3-33*B*c*d^2+18*C*c^2*d+37*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^3-1/8*a*b*(A*b^2*c*(-3*a*d^2+4*b*c^2)-a*(b^2*c^2*(-6*B*d+C*c)-4*a^2*d^3*D-a*b*d*(-B*d^2+6*C*c*d-3*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(9/2),1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^7,x,7,-1/16*b*(A*b*(a^2*d^4-12*a*b*c^2*d^2+8*b^2*c^4)-a*(2*b^2*c^3*(-7*B*d+C*c)+2*a^2*d^3*(C*d-7*D*c)-a*b*c*d*(-7*B*d^2+17*C*c*d-7*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^5/(d*x+c)^2-1/6*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^6+1/10*(2*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-3*A*d^3+B*c*d^2+C*c^2*d-3*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^5-1/40*(10*a^2*d^4*(C*d-3*D*c)-2*b^2*c^2*(-8*A*d^3+B*c*d^2+C*c^2*d+2*D*c^3)-a*b*d^2*(5*A*d^3-19*B*c*d^2+13*C*c^2*d+13*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^4-1/120*(40*a^3*d^6*D+2*a^2*b*d^4*(-8*B*d^2+41*C*c*d-39*D*c^2)-2*b^3*c^3*(-28*A*d^3+B*c*d^2+C*c^2*d+2*D*c^3)-a*b^2*c*d^2*(49*A*d^3-87*B*c*d^2+25*C*c^2*d+17*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^4/(d*x+c)^3-1/16*a*b^2*(A*b*(a^2*d^4-12*a*b*c^2*d^2+8*b^2*c^4)-a*(2*b^2*c^3*(-7*B*d+C*c)+2*a^2*d^3*(C*d-7*D*c)-a*b*c*d*(-7*B*d^2+17*C*c*d-7*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(11/2),1],
[sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^8,x,8,-1/16*b*(A*b^2*c*(5*a^2*d^4-20*a*b*c^2*d^2+8*b^2*c^4)-a*(2*b^3*c^4*(-8*B*d+C*c)+2*a^3*d^5*D+a^2*b*d^3*(-B*d^2+8*C*c*d-23*D*c^2)-a*b^2*c^2*d*(-16*B*d^2+23*C*c*d-8*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^6/(d*x+c)^2-1/7*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^7+1/42*(7*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-11*A*d^3+4*B*c*d^2+3*C*c^2*d-10*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^6-1/70*(14*a^2*d^4*(C*d-3*D*c)-b^2*c^2*(-25*A*d^3+4*B*c*d^2+3*C*c^2*d+4*D*c^3)-a*b*d^2*(8*A*d^3-29*B*c*d^2+22*C*c^2*d+13*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^5-1/280*(70*a^3*d^6*D+7*a^2*b*d^4*(-5*B*d^2+24*C*c*d-27*D*c^2)-2*b^3*c^3*(-60*A*d^3+4*B*c*d^2+3*C*c^2*d+4*D*c^3)-a*b^2*c*d^2*(111*A*d^3-188*B*c*d^2+69*C*c^2*d+36*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^4/(d*x+c)^4+1/840*b*(14*a^3*d^6*(8*C*d-49*D*c)-a^2*b*d^4*(64*A*d^3-407*B*c*d^2+904*C*c^2*d-505*D*c^3)+2*b^3*c^4*(-200*A*d^3+4*B*c*d^2+3*C*c^2*d+4*D*c^3)+a*b^2*c^2*d^2*(691*A*d^3-740*B*c*d^2+145*C*c^2*d+44*D*c^3))*(b*x^2+a)^(3/2)/d^2/(a*d^2+b*c^2)^5/(d*x+c)^3-1/16*a*b^2*(A*b^2*c*(5*a^2*d^4-20*a*b*c^2*d^2+8*b^2*c^4)-a*(2*b^3*c^4*(-8*B*d+C*c)+2*a^3*d^5*D+a^2*b*d^3*(-B*d^2+8*C*c*d-23*D*c^2)-a*b^2*c^2*d*(-16*B*d^2+23*C*c*d-8*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(13/2),1],
[(d*x+c)^3*(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A),x,11,1/256*a*(96*A*b^3*c^3-a*(16*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+3*a^2*d^3*D-6*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x*sqrt(b*x^2+a)/b^3+1/384*(96*A*b^3*c^3-a*(16*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+3*a^2*d^3*D-6*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x*(b*x^2+a)^(3/2)/b^3+1/5*(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*(b*x^2+a)^(5/2)/b^3+1/96*(16*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+3*a^2*d^3*D-6*a*b*d*(B*d^2+3*C*c*d+3*D*c^2))*x*(b*x^2+a)^(5/2)/b^3-1/16*d*(a*d^2*D-2*b*(B*d^2+3*C*c*d+3*D*c^2))*x^3*(b*x^2+a)^(5/2)/b^2+1/10*d^3*D*x^5*(b*x^2+a)^(5/2)/b-1/7*(2*a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*(b*x^2+a)^(7/2)/b^3+1/9*d^2*(C*d+3*D*c)*(b*x^2+a)^(9/2)/b^3+1/256*a^2*(96*A*b^3*c^3-a*(16*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+3*a^2*d^3*D-6*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x+c)^2*(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A),x,10,1/128*a*(8*A*b*(-a*d^2+6*b*c^2)-a*(8*b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*x*sqrt(b*x^2+a)/b^2+1/192*(8*A*b*(-a*d^2+6*b*c^2)-a*(8*b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*x*(b*x^2+a)^(3/2)/b^2+1/5*(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))*(b*x^2+a)^(5/2)/b^3+1/48*(8*b*(A*d^2+2*B*c*d+C*c^2)-3*a*d*(C*d+2*D*c))*x*(b*x^2+a)^(5/2)/b^2+1/8*d*(C*d+2*D*c)*x^3*(b*x^2+a)^(5/2)/b-1/7*(2*a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))*(b*x^2+a)^(7/2)/b^3+1/9*d^2*D*(b*x^2+a)^(9/2)/b^3+1/128*a^2*(8*A*b*(-a*d^2+6*b*c^2)-a*(8*b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)*(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A),x,10,1/128*a*(48*A*b^2*c-a*(8*b*(B*d+C*c)-3*a*d*D))*x*sqrt(b*x^2+a)/b^2+1/192*(48*A*b^2*c-a*(8*b*(B*d+C*c)-3*a*d*D))*x*(b*x^2+a)^(3/2)/b^2+1/5*(A*b*d+B*b*c-C*a*d-D*a*c)*(b*x^2+a)^(5/2)/b^2+1/48*(8*b*(B*d+C*c)-3*a*d*D)*x*(b*x^2+a)^(5/2)/b^2+1/8*d*D*x^3*(b*x^2+a)^(5/2)/b+1/7*(C*d+D*c)*(b*x^2+a)^(7/2)/b^2+1/128*a^2*(48*A*b^2*c-a*(8*b*(B*d+C*c)-3*a*d*D))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A),x,9,1/16*a*(6*A*b-C*a)*x*sqrt(b*x^2+a)/b+1/24*(6*A*b-C*a)*x*(b*x^2+a)^(3/2)/b+1/5*(B*b-D*a)*(b*x^2+a)^(5/2)/b^2+1/6*C*x*(b*x^2+a)^(5/2)/b+1/7*D*(b*x^2+a)^(7/2)/b^2+1/16*a^2*(6*A*b-C*a)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c),x,11,(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^6-1/16*(a^2*d^3*D+6*a*b*d*(-B*d^2+C*c*d-D*c^2)+8*b^2*c*(c^2*C-B*c*d+A*d^2-c^3*D/d))*x*sqrt(b*x^2+a)/b/d^4+1/3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(3/2)/d^4-1/24*(a*d^2*D+6*b*(-B*d^2+C*c*d-D*c^2))*x*(b*x^2+a)^(3/2)/b/d^3+1/30*(6*C*d-11*D*c)*(b*x^2+a)^(5/2)/b/d^2+1/6*D*(d*x+c)*(b*x^2+a)^(5/2)/b/d^2-1/16*(a^3*d^6*D+6*a^2*b*d^4*(-B*d^2+C*c*d-D*c^2)+16*b^3*c^3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+24*a*b^2*c*d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/d^7-(a*d^2+b*c^2)^(3/2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^7,1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^2,x,11,1/15*(3*a^2*d^4*D-20*a*b*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-15*b^2*c*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))*sqrt(b*x^2+a)/b/d^6+1/8*(5*a*d^2*(C*d-2*D*c)+4*b*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x*sqrt(b*x^2+a)/d^5+1/15*(6*a*d^2*D-5*b*(-B*d^2+2*C*c*d-3*D*c^2))*x^2*sqrt(b*x^2+a)/d^4+1/4*b*(C*d-2*D*c)*x^3*sqrt(b*x^2+a)/d^3+1/5*b*D*x^4*sqrt(b*x^2+a)/d^2-(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^6/(d*x+c)+1/8*(3*a^2*d^4*(C*d-2*D*c)+8*b^2*c^2*(3*A*d^3-4*B*c*d^2+5*C*c^2*d-6*D*c^3)+12*a*b*d^2*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/d^7+sqrt(a*d^2+b*c^2)*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(3*A*d^3-4*B*c*d^2+5*C*c^2*d-6*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^7,1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^3,x,11,1/3*(4*a*d^2*(C*d-3*D*c)+3*b*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*sqrt(b*x^2+a)/d^6+1/8*(5*a*d^2*D-4*b*(-B*d^2+3*C*c*d-6*D*c^2))*x*sqrt(b*x^2+a)/d^5+1/3*b*(C*d-3*D*c)*x^2*sqrt(b*x^2+a)/d^4+1/4*b*D*x^3*sqrt(b*x^2+a)/d^3-1/2*(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^6/(d*x+c)^2+1/2*(2*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(5*A*d^3-7*B*c*d^2+9*C*c^2*d-11*D*c^3))*sqrt(b*x^2+a)/d^6/(d*x+c)+1/8*(3*a^2*d^4*D-12*a*b*d^2*(-B*d^2+3*C*c*d-6*D*c^2)-8*b^2*c*(3*A*d^3-6*B*c*d^2+10*C*c^2*d-15*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/d^7-1/2*(2*a^2*d^4*(C*d-3*D*c)+a*b*d^2*(3*A*d^3-9*B*c*d^2+19*C*c^2*d-33*D*c^3)+2*b^2*c^2*(3*A*d^3-6*B*c*d^2+10*C*c^2*d-15*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^7/sqrt(a*d^2+b*c^2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^4,x,11,1/3*(4*a*d^2*D-3*b*(-B*d^2+4*C*c*d-10*D*c^2))*sqrt(b*x^2+a)/d^6+1/2*b*(C*d-4*D*c)*x*sqrt(b*x^2+a)/d^5+1/3*b*D*x^2*sqrt(b*x^2+a)/d^4-1/3*(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^6/(d*x+c)^3+1/6*(3*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(7*A*d^3-10*B*c*d^2+13*C*c^2*d-16*D*c^3))*sqrt(b*x^2+a)/d^6/(d*x+c)^2-1/6*(6*a^2*d^4*(C*d-3*D*c)+a*b*d^2*(8*A*d^3-23*B*c*d^2+50*C*c^2*d-89*D*c^3)+b^2*c^2*(11*A*d^3-26*B*c*d^2+47*C*c^2*d-74*D*c^3))*sqrt(b*x^2+a)/d^6/(a*d^2+b*c^2)/(d*x+c)+1/2*sqrt(b)*(3*a*d^2*(C*d-4*D*c)+b*(2*A*d^3-8*B*c*d^2+20*C*c^2*d-40*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^7-1/2*(2*a^3*d^6*D-3*a^2*b*d^4*(-B*d^2+4*C*c*d-11*D*c^2)-3*a*b^2*c*d^2*(A*d^3-4*B*c*d^2+11*C*c^2*d-24*D*c^3)-2*b^3*c^3*(A*d^3-4*B*c*d^2+10*C*c^2*d-20*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^7/(a*d^2+b*c^2)^(3/2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^5,x,11,b*(C*d-5*D*c)*sqrt(b*x^2+a)/d^6+1/2*b*D*x*sqrt(b*x^2+a)/d^5-1/4*(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^6/(d*x+c)^4+1/12*(4*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(9*A*d^3-13*B*c*d^2+17*C*c^2*d-21*D*c^3))*sqrt(b*x^2+a)/d^6/(d*x+c)^3-1/24*(12*a^2*d^4*(C*d-3*D*c)+a*b*d^2*(15*A*d^3-43*B*c*d^2+95*C*c^2*d-171*D*c^3)+2*b^2*c^2*(9*A*d^3-23*B*c*d^2+43*C*c^2*d-69*D*c^3))*sqrt(b*x^2+a)/d^6/(a*d^2+b*c^2)/(d*x+c)^2-1/24*(24*a^3*d^6*D-4*a^2*b*d^4*(-8*B*d^2+31*C*c*d-87*D*c^2)-a*b^2*c*d^2*(15*A*d^3-91*B*c*d^2+287*C*c^2*d-675*D*c^3)-2*b^3*c^3*(3*A*d^3-25*B*c*d^2+77*C*c^2*d-171*D*c^3))*sqrt(b*x^2+a)/d^6/(a*d^2+b*c^2)^2/(d*x+c)+1/2*sqrt(b)*(3*a*d^2*D-2*b*(-B*d^2+5*C*c*d-15*D*c^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^7-1/8*b*(12*a^3*d^6*(C*d-5*D*c)+4*a*b^2*c^3*d^2*(-5*B*d^2+25*C*c*d-78*D*c^2)+8*b^3*c^5*(-B*d^2+5*C*c*d-15*D*c^2)+3*a^2*b*d^4*(A*d^3-5*B*c*d^2+25*C*c^2*d-85*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^7/(a*d^2+b*c^2)^(5/2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^6,x,11,b*D*sqrt(b*x^2+a)/d^6+1/4*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*(-A*c*d^3+C*c^3*d-2*D*c^4))*sqrt(b*x^2+a)/d^6/(d*x+c)^4-1/12*(4*a^2*d^4*(C*d-3*D*c)+a*b*c*d^2*(-9*B*d^2+26*C*c*d-51*D*c^2)+b^2*(-9*A*c^2*d^3+13*C*c^4*d-30*D*c^5))*sqrt(b*x^2+a)/d^6/(a*d^2+b*c^2)/(d*x+c)^3-1/24*(12*a^3*d^6*D-a^2*b*d^4*(-15*B*d^2+58*C*c*d-165*D*c^2)-a*b^2*c*d^2*(-15*A*d^3-18*B*c*d^2+107*C*c^2*d-288*D*c^3)-2*b^3*(-9*A*c^3*d^3+23*C*c^5*d-66*D*c^6))*sqrt(b*x^2+a)/d^6/(a*d^2+b*c^2)^2/(d*x+c)^2-1/24*b*(4*a^3*d^6*(8*C*d-39*D*c)+3*a^2*b*c*d^4*(-5*B*d^2+46*C*c*d-183*D*c^2)+3*a*b^2*c^2*d^2*(-5*A*d^3-2*B*c*d^2+49*C*c^2*d-196*D*c^3)+b^3*(-6*A*c^4*d^3+50*C*c^6*d-204*D*c^7))*sqrt(b*x^2+a)/d^6/(a*d^2+b*c^2)^3/(d*x+c)-1/5*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^5+b^(3/2)*(C*d-6*D*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^7-1/8*b*(12*a^4*d^8*D-8*b^4*c^7*(C*d-6*D*c)-28*a*b^3*c^5*d^2*(C*d-6*D*c)-3*a^3*b*d^6*(-B*d^2+6*C*c*d-35*D*c^2)-a^2*b^2*c*d^4*(-3*A*d^3+35*C*c^2*d-210*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^7/(a*d^2+b*c^2)^(7/2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^7,x,9,-1/16*b*(16*b^4*c^9*D+56*a*b^3*c^7*d^2*D+2*a^4*d^8*(3*C*d-5*D*c)-a^3*b*d^6*(A*d^3-7*B*c*d^2+C*c^2*d-23*D*c^3)+6*a^2*b^2*c^2*d^4*(A*d^3+11*D*c^3)+d*(24*b^4*c^8*D+16*a^4*d^8*D-6*a^3*b*c*d^6*(C*d-15*D*c)-2*a*b^3*c^3*d^2*(3*A*d^3-47*D*c^3)+a^2*b^2*c*d^4*(A*d^3-7*B*c*d^2+C*c^2*d+137*D*c^3))*x)*sqrt(b*x^2+a)/d^6/(a*d^2+b*c^2)^4/(d*x+c)^2-1/24*(8*b^3*c^7*D+2*a^3*d^6*(3*C*d-5*D*c)-a^2*b*d^4*(A*d^3-7*B*c*d^2+C*c^2*d-7*D*c^3)+6*a*b^2*c^2*d^2*(A*d^3+3*D*c^3)-d*(A*b^2*c*d^3*(-a*d^2+6*b*c^2)-14*b^3*c^6*D-8*a^3*d^6*D+6*a^2*b*c*d^4*(C*d-7*D*c)-a*b^2*c^2*d^2*(-7*B*d^2+C*c*d+41*D*c^2))*x)*(b*x^2+a)^(3/2)/d^4/(a*d^2+b*c^2)^3/(d*x+c)^4-1/6*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^6+1/30*(6*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-7*A*d^3+B*c*d^2+5*C*c^2*d-11*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^5+b^(3/2)*D*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^7+1/16*b^2*(16*b^4*c^9*D+72*a*b^3*c^7*d^2*D-6*a^4*d^8*(C*d-7*D*c)-6*a^2*b^2*c^2*d^4*(A*d^3-21*D*c^3)+a^3*b*d^6*(A*d^3-7*B*c*d^2+C*c^2*d+105*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^7/(a*d^2+b*c^2)^(9/2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^8,x,7,-1/16*a*b*(3*A*b^2*c*(-a*d^2+2*b*c^2)-a*(b^2*c^2*(-8*B*d+C*c)-6*a^2*d^3*D-a*b*d*(-B*d^2+8*C*c*d-3*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^5/(d*x+c)^2-1/24*(3*A*b^2*c*(-a*d^2+2*b*c^2)-a*(b^2*c^2*(-8*B*d+C*c)-6*a^2*d^3*D-a*b*d*(-B*d^2+8*C*c*d-3*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^4/(d*x+c)^4-1/7*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^7+1/42*(7*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-9*A*d^3+2*B*c*d^2+5*C*c^2*d-12*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^6-1/210*(42*a^2*d^4*(C*d-3*D*c)-b^2*c^2*(-51*A*d^3+2*B*c*d^2+5*C*c^2*d+30*D*c^3)-a*b*d^2*(12*A*d^3-61*B*c*d^2+26*C*c^2*d+93*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^5-1/16*a^2*b^2*(3*A*b^2*c*(-a*d^2+2*b*c^2)-a*(b^2*c^2*(-8*B*d+C*c)-6*a^2*d^3*D-a*b*d*(-B*d^2+8*C*c*d-3*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(11/2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^9,x,8,-1/128*a*b^2*(3*A*b*(a^2*d^4-16*a*b*c^2*d^2+16*b^2*c^4)-a*(8*b^2*c^3*(-9*B*d+C*c)+8*a^2*d^3*(C*d-9*D*c)-a*b*c*d*(-27*B*d^2+83*C*c*d-27*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^6/(d*x+c)^2-1/192*b*(3*A*b*(a^2*d^4-16*a*b*c^2*d^2+16*b^2*c^4)-a*(8*b^2*c^3*(-9*B*d+C*c)+8*a^2*d^3*(C*d-9*D*c)-a*b*c*d*(-27*B*d^2+83*C*c*d-27*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^5/(d*x+c)^4-1/8*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^8+1/56*(8*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-11*A*d^3+3*B*c*d^2+5*C*c^2*d-13*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^7-1/336*(56*a^2*d^4*(C*d-3*D*c)-2*b^2*c^2*(-39*A*d^3+3*B*c*d^2+5*C*c^2*d+15*D*c^3)-a*b*d^2*(21*A*d^3-93*B*c*d^2+53*C*c^2*d+99*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^6-1/1680*(336*a^3*d^6*D+8*a^2*b*d^4*(-12*B*d^2+73*C*c*d-57*D*c^2)-2*b^3*c^3*(-207*A*d^3+3*B*c*d^2+5*C*c^2*d+15*D*c^3)-a*b^2*c*d^2*(279*A*d^3-591*B*c*d^2+119*C*c^2*d+129*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^4/(d*x+c)^5-1/128*a^2*b^3*(3*A*b*(a^2*d^4-16*a*b*c^2*d^2+16*b^2*c^4)-a*(8*b^2*c^3*(-9*B*d+C*c)+8*a^2*d^3*(C*d-9*D*c)-a*b*c*d*(-27*B*d^2+83*C*c*d-27*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(13/2),1],
[(b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^10,x,9,-1/128*a*b^2*(A*b^2*c*(15*a^2*d^4-80*a*b*c^2*d^2+48*b^2*c^4)-a*(8*b^3*c^4*(-10*B*d+C*c)+8*a^3*d^5*D+3*a^2*b*d^3*(-B*d^2+10*C*c*d-35*D*c^2)-15*a*b^2*c^2*d*(-4*B*d^2+7*C*c*d-2*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^7/(d*x+c)^2-1/192*b*(A*b^2*c*(15*a^2*d^4-80*a*b*c^2*d^2+48*b^2*c^4)-a*(8*b^3*c^4*(-10*B*d+C*c)+8*a^3*d^5*D+3*a^2*b*d^3*(-B*d^2+10*C*c*d-35*D*c^2)-15*a*b^2*c^2*d*(-4*B*d^2+7*C*c*d-2*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^6/(d*x+c)^4-1/9*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^9+1/72*(9*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-13*A*d^3+4*B*c*d^2+5*C*c^2*d-14*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^8-1/504*(72*a^2*d^4*(C*d-3*D*c)-3*b^2*c^2*(-37*A*d^3+4*B*c*d^2+5*C*c^2*d+10*D*c^3)-a*b*d^2*(32*A*d^3-131*B*c*d^2+86*C*c^2*d+103*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^7-1/1008*(168*a^3*d^6*D+9*a^2*b*d^4*(-7*B*d^2+38*C*c*d-37*D*c^2)-2*b^3*c^3*(-121*A*d^3+4*B*c*d^2+5*C*c^2*d+10*D*c^3)-a*b^2*c*d^2*(187*A*d^3-358*B*c*d^2+97*C*c^2*d+92*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^4/(d*x+c)^6+1/5040*b*(24*a^3*d^6*(12*C*d-85*D*c)-a^2*b*d^4*(128*A*d^3-965*B*c*d^2+2450*C*c^2*d-1055*D*c^3)+2*b^3*c^4*(-625*A*d^3+4*B*c*d^2+5*C*c^2*d+10*D*c^3)+a*b^2*c^2*d^2*(1625*A*d^3-2030*B*c*d^2+275*C*c^2*d+112*D*c^3))*(b*x^2+a)^(5/2)/d^2/(a*d^2+b*c^2)^5/(d*x+c)^5-1/128*a^2*b^3*(A*b^2*c*(15*a^2*d^4-80*a*b*c^2*d^2+48*b^2*c^4)-a*(8*b^3*c^4*(-10*B*d+C*c)+8*a^3*d^5*D+3*a^2*b*d^3*(-B*d^2+10*C*c*d-35*D*c^2)-15*a*b^2*c^2*d*(-4*B*d^2+7*C*c*d-2*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(15/2),1],
[(d*x+c)^3*(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A),x,12,1/1024*a^2*(320*A*b^3*c^3-a*(40*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-12*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x*sqrt(b*x^2+a)/b^3+1/1536*a*(320*A*b^3*c^3-a*(40*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-12*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x*(b*x^2+a)^(3/2)/b^3+1/1920*(320*A*b^3*c^3-a*(40*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-12*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x*(b*x^2+a)^(5/2)/b^3+1/7*(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*(b*x^2+a)^(7/2)/b^3+1/320*(40*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-12*a*b*d*(B*d^2+3*C*c*d+3*D*c^2))*x*(b*x^2+a)^(7/2)/b^3-1/120*d*(5*a*d^2*D-12*b*(B*d^2+3*C*c*d+3*D*c^2))*x^3*(b*x^2+a)^(7/2)/b^2+1/12*d^3*D*x^5*(b*x^2+a)^(7/2)/b-1/9*(2*a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*(b*x^2+a)^(9/2)/b^3+1/11*d^2*(C*d+3*D*c)*(b*x^2+a)^(11/2)/b^3+1/1024*a^3*(320*A*b^3*c^3-a*(40*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-12*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x+c)^2*(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A),x,11,1/256*a^2*(10*A*b*(-a*d^2+8*b*c^2)-a*(10*b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*x*sqrt(b*x^2+a)/b^2+1/384*a*(10*A*b*(-a*d^2+8*b*c^2)-a*(10*b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*x*(b*x^2+a)^(3/2)/b^2+1/480*(10*A*b*(-a*d^2+8*b*c^2)-a*(10*b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*x*(b*x^2+a)^(5/2)/b^2+1/7*(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))*(b*x^2+a)^(7/2)/b^3+1/80*(10*b*(A*d^2+2*B*c*d+C*c^2)-3*a*d*(C*d+2*D*c))*x*(b*x^2+a)^(7/2)/b^2+1/10*d*(C*d+2*D*c)*x^3*(b*x^2+a)^(7/2)/b-1/9*(2*a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))*(b*x^2+a)^(9/2)/b^3+1/11*d^2*D*(b*x^2+a)^(11/2)/b^3+1/256*a^3*(10*A*b*(-a*d^2+8*b*c^2)-a*(10*b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)*(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A),x,11,1/256*a^2*(80*A*b^2*c-a*(10*b*(B*d+C*c)-3*a*d*D))*x*sqrt(b*x^2+a)/b^2+1/384*a*(80*A*b^2*c-a*(10*b*(B*d+C*c)-3*a*d*D))*x*(b*x^2+a)^(3/2)/b^2+1/480*(80*A*b^2*c-a*(10*b*(B*d+C*c)-3*a*d*D))*x*(b*x^2+a)^(5/2)/b^2+1/7*(A*b*d+B*b*c-C*a*d-D*a*c)*(b*x^2+a)^(7/2)/b^2+1/80*(10*b*(B*d+C*c)-3*a*d*D)*x*(b*x^2+a)^(7/2)/b^2+1/10*d*D*x^3*(b*x^2+a)^(7/2)/b+1/9*(C*d+D*c)*(b*x^2+a)^(9/2)/b^2+1/256*a^3*(80*A*b^2*c-a*(10*b*(B*d+C*c)-3*a*d*D))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A),x,10,5/128*a^2*(8*A*b-C*a)*x*sqrt(b*x^2+a)/b+5/192*a*(8*A*b-C*a)*x*(b*x^2+a)^(3/2)/b+1/48*(8*A*b-C*a)*x*(b*x^2+a)^(5/2)/b+1/7*(B*b-D*a)*(b*x^2+a)^(7/2)/b^2+1/8*C*x*(b*x^2+a)^(7/2)/b+1/9*D*(b*x^2+a)^(9/2)/b^2+5/128*a^3*(8*A*b-C*a)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c),x,13,(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^8-1/128*(5*a^3*d^6*D+40*a^2*b*d^4*(-B*d^2+C*c*d-D*c^2)+64*b^3*c^3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+112*a*b^2*c*d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x*sqrt(b*x^2+a)/b/d^7+1/3*(a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(3/2)/d^6-1/192*(5*a^2*d^4*D+40*a*b*d^2*(-B*d^2+C*c*d-D*c^2)+48*b^2*c*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x*(b*x^2+a)^(3/2)/b/d^5+1/5*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(5/2)/d^4-1/48*(a*d^2*D+8*b*(-B*d^2+C*c*d-D*c^2))*x*(b*x^2+a)^(5/2)/b/d^3+1/56*(8*C*d-15*D*c)*(b*x^2+a)^(7/2)/b/d^2+1/8*D*(d*x+c)*(b*x^2+a)^(7/2)/b/d^2-1/128*(5*a^4*d^8*D+40*a^3*b*d^6*(-B*d^2+C*c*d-D*c^2)+128*b^4*c^5*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+320*a*b^3*c^3*d^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)+240*a^2*b^2*c*d^4*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/d^9-(a*d^2+b*c^2)^(5/2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9,1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^2,x,13,1/105*(15*a^3*d^6*D-161*a^2*b*d^4*(-B*d^2+2*C*c*d-3*D*c^2)-105*b^3*c^3*(4*A*d^3-5*B*c*d^2+6*C*c^2*d-7*D*c^3)-245*a*b^2*c*d^2*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))*sqrt(b*x^2+a)/b/d^8+1/16*(11*a^2*d^4*(C*d-2*D*c)+8*b^2*c^2*(3*A*d^3-4*B*c*d^2+5*C*c^2*d-6*D*c^3)+18*a*b*d^2*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x*sqrt(b*x^2+a)/d^7+1/105*(45*a^2*d^4*D-77*a*b*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-35*b^2*c*(2*A*d^3-3*B*c*d^2+4*C*c^2*d-5*D*c^3))*x^2*sqrt(b*x^2+a)/d^6+1/24*b*(13*a*d^2*(C*d-2*D*c)+6*b*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*x^3*sqrt(b*x^2+a)/d^5+1/35*b*(15*a*d^2*D-7*b*(-B*d^2+2*C*c*d-3*D*c^2))*x^4*sqrt(b*x^2+a)/d^4+1/6*b^2*(C*d-2*D*c)*x^5*sqrt(b*x^2+a)/d^3+1/7*b^2*D*x^6*sqrt(b*x^2+a)/d^2-(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^8/(d*x+c)+1/16*(5*a^3*d^6*(C*d-2*D*c)+16*b^3*c^4*(5*A*d^3-6*B*c*d^2+7*C*c^2*d-8*D*c^3)+40*a*b^2*c^2*d^2*(3*A*d^3-4*B*c*d^2+5*C*c^2*d-6*D*c^3)+30*a^2*b*d^4*(A*d^3-2*B*c*d^2+3*C*c^2*d-4*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/d^9+(a*d^2+b*c^2)^(3/2)*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(5*A*d^3-6*B*c*d^2+7*C*c^2*d-8*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9,1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^3,x,13,1/15*(23*a^2*d^4*(C*d-3*D*c)+15*b^2*c^2*(6*A*d^3-10*B*c*d^2+15*C*c^2*d-21*D*c^3)+35*a*b*d^2*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*sqrt(b*x^2+a)/d^8+1/16*(11*a^2*d^4*D-18*a*b*d^2*(-B*d^2+3*C*c*d-6*D*c^2)-8*b^2*c*(3*A*d^3-6*B*c*d^2+10*C*c^2*d-15*D*c^3))*x*sqrt(b*x^2+a)/d^7+1/15*b*(11*a*d^2*(C*d-3*D*c)+5*b*(A*d^3-3*B*c*d^2+6*C*c^2*d-10*D*c^3))*x^2*sqrt(b*x^2+a)/d^6+1/24*b*(13*a*d^2*D-6*b*(-B*d^2+3*C*c*d-6*D*c^2))*x^3*sqrt(b*x^2+a)/d^5+1/5*b^2*(C*d-3*D*c)*x^4*sqrt(b*x^2+a)/d^4+1/6*b^2*D*x^5*sqrt(b*x^2+a)/d^3-1/2*(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^8/(d*x+c)^2+1/2*(a*d^2+b*c^2)*(2*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(9*A*d^3-11*B*c*d^2+13*C*c^2*d-15*D*c^3))*sqrt(b*x^2+a)/d^8/(d*x+c)+1/16*(5*a^3*d^6*D-30*a^2*b*d^4*(-B*d^2+3*C*c*d-6*D*c^2)-16*b^3*c^3*(10*A*d^3-15*B*c*d^2+21*C*c^2*d-28*D*c^3)-40*a*b^2*c*d^2*(3*A*d^3-6*B*c*d^2+10*C*c^2*d-15*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/d^9-1/2*sqrt(a*d^2+b*c^2)*(2*a^2*d^4*(C*d-3*D*c)+a*b*d^2*(5*A*d^3-15*B*c*d^2+29*C*c^2*d-47*D*c^3)+2*b^2*c^2*(10*A*d^3-15*B*c*d^2+21*C*c^2*d-28*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9,1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^4,x,13,1/15*(23*a^2*d^4*D-35*a*b*d^2*(-B*d^2+4*C*c*d-10*D*c^2)-15*b^2*c*(4*A*d^3-10*B*c*d^2+20*C*c^2*d-35*D*c^3))*sqrt(b*x^2+a)/d^8+1/8*b*(9*a*d^2*(C*d-4*D*c)+4*b*(A*d^3-4*B*c*d^2+10*C*c^2*d-20*D*c^3))*x*sqrt(b*x^2+a)/d^7+1/15*b*(11*a*d^2*D-5*b*(-B*d^2+4*C*c*d-10*D*c^2))*x^2*sqrt(b*x^2+a)/d^6+1/4*b^2*(C*d-4*D*c)*x^3*sqrt(b*x^2+a)/d^5+1/5*b^2*D*x^4*sqrt(b*x^2+a)/d^4-1/3*(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^8/(d*x+c)^3+1/6*(a*d^2+b*c^2)*(3*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(13*A*d^3-16*B*c*d^2+19*C*c^2*d-22*D*c^3))*sqrt(b*x^2+a)/d^8/(d*x+c)^2-1/6*(6*a^2*d^4*(C*d-3*D*c)+b^2*c^2*(47*A*d^3-74*B*c*d^2+107*C*c^2*d-146*D*c^3)+a*b*d^2*(14*A*d^3-41*B*c*d^2+80*C*c^2*d-131*D*c^3))*sqrt(b*x^2+a)/d^8/(d*x+c)+1/8*sqrt(b)*(15*a^2*d^4*(C*d-4*D*c)+8*b^2*c^2*(10*A*d^3-20*B*c*d^2+35*C*c^2*d-56*D*c^3)+20*a*b*d^2*(A*d^3-4*B*c*d^2+10*C*c^2*d-20*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^9-1/2*(2*a^3*d^6*D-a^2*b*d^4*(-5*B*d^2+20*C*c*d-51*D*c^2)-a*b^2*c*d^2*(15*A*d^3-40*B*c*d^2+85*C*c^2*d-156*D*c^3)-2*b^3*c^3*(10*A*d^3-20*B*c*d^2+35*C*c^2*d-56*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9/sqrt(a*d^2+b*c^2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^5,x,13,1/3*b*(7*a*d^2*(C*d-5*D*c)+3*b*(A*d^3-5*B*c*d^2+15*C*c^2*d-35*D*c^3))*sqrt(b*x^2+a)/d^8+1/8*b*(9*a*d^2*D-4*b*(-B*d^2+5*C*c*d-15*D*c^2))*x*sqrt(b*x^2+a)/d^7+1/3*b^2*(C*d-5*D*c)*x^2*sqrt(b*x^2+a)/d^6+1/4*b^2*D*x^3*sqrt(b*x^2+a)/d^5-1/4*(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^8/(d*x+c)^4+1/12*(a*d^2+b*c^2)*(4*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(17*A*d^3-21*B*c*d^2+25*C*c^2*d-29*D*c^3))*sqrt(b*x^2+a)/d^8/(d*x+c)^3-1/24*(12*a^2*d^4*(C*d-3*D*c)+a*b*d^2*(27*A*d^3-79*B*c*d^2+155*C*c^2*d-255*D*c^3)+2*b^2*c^2*(43*A*d^3-69*B*c*d^2+101*C*c^2*d-139*D*c^3))*sqrt(b*x^2+a)/d^8/(d*x+c)^2-1/24*(24*a^3*d^6*D-4*a^2*b*d^4*(-14*B*d^2+55*C*c*d-141*D*c^2)-a*b^2*c*d^2*(139*A*d^3-383*B*c*d^2+843*C*c^2*d-1591*D*c^3)-2*b^3*c^3*(77*A*d^3-171*B*c*d^2+319*C*c^2*d-533*D*c^3))*sqrt(b*x^2+a)/d^8/(a*d^2+b*c^2)/(d*x+c)+5/8*sqrt(b)*(3*a^2*d^4*D-4*a*b*d^2*(-B*d^2+5*C*c*d-15*D*c^2)-8*b^2*c*(A*d^3-3*B*c*d^2+7*C*c^2*d-14*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^9-5/8*b*(4*a^3*d^6*(C*d-5*D*c)+4*a*b^2*c^2*d^2*(3*A*d^3-10*B*c*d^2+26*C*c^2*d-57*D*c^3)+3*a^2*b*d^4*(A*d^3-5*B*c*d^2+17*C*c^2*d-45*D*c^3)+8*b^3*c^4*(A*d^3-3*B*c*d^2+7*C*c^2*d-14*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9/(a*d^2+b*c^2)^(3/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^6,x,13,1/3*b*(7*a*d^2*D-3*b*(-B*d^2+6*C*c*d-21*D*c^2))*sqrt(b*x^2+a)/d^8+1/2*b^2*(C*d-6*D*c)*x*sqrt(b*x^2+a)/d^7+1/3*b^2*D*x^2*sqrt(b*x^2+a)/d^6-1/5*(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^8/(d*x+c)^5+1/20*(a*d^2+b*c^2)*(5*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(21*A*d^3-26*B*c*d^2+31*C*c^2*d-36*D*c^3))*sqrt(b*x^2+a)/d^8/(d*x+c)^4-1/60*(20*a^2*d^4*(C*d-3*D*c)+b^2*c^2*(137*A*d^3-222*B*c*d^2+327*C*c^2*d-452*D*c^3)+a*b*d^2*(44*A*d^3-129*B*c*d^2+254*C*c^2*d-419*D*c^3))*sqrt(b*x^2+a)/d^8/(d*x+c)^3-1/120*(60*a^3*d^6*D-5*a^2*b*d^4*(-27*B*d^2+106*C*c*d-273*D*c^2)-a*b^2*c*d^2*(311*A*d^3-876*B*c*d^2+1961*C*c^2*d-3746*D*c^3)-2*b^3*c^3*(163*A*d^3-378*B*c*d^2+723*C*c^2*d-1228*D*c^3))*sqrt(b*x^2+a)/d^8/(a*d^2+b*c^2)/(d*x+c)^2-1/120*b*(20*a^3*d^6*(14*C*d-69*D*c)+a*b^2*c^2*d^2*(503*A*d^3-1968*B*c*d^2+5593*C*c^2*d-12998*D*c^3)+a^2*b*d^4*(184*A*d^3-879*B*c*d^2+3074*C*c^2*d-8389*D*c^3)+2*b^3*c^4*(137*A*d^3-522*B*c*d^2+1377*C*c^2*d-2972*D*c^3))*sqrt(b*x^2+a)/d^8/(a*d^2+b*c^2)^2/(d*x+c)+1/2*b^(3/2)*(5*a*d^2*(C*d-6*D*c)+2*b*(A*d^3-6*B*c*d^2+21*C*c^2*d-56*D*c^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^9-1/8*b*(20*a^4*d^8*D-5*a^3*b*d^6*(-3*B*d^2+18*C*c*d-73*D*c^2)-5*a^2*b^2*c*d^4*(3*A*d^3-18*B*c*d^2+73*C*c^2*d-228*D*c^3)-20*a*b^3*c^3*d^2*(A*d^3-6*B*c*d^2+22*C*c^2*d-62*D*c^3)-8*b^4*c^5*(A*d^3-6*B*c*d^2+21*C*c^2*d-56*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9/(a*d^2+b*c^2)^(5/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^7,x,13,b^2*(C*d-7*D*c)*sqrt(b*x^2+a)/d^8+1/2*b^2*D*x*sqrt(b*x^2+a)/d^7-1/6*(a*d^2+b*c^2)^2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^8/(d*x+c)^6+1/30*(a*d^2+b*c^2)*(6*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(25*A*d^3-31*B*c*d^2+37*C*c^2*d-43*D*c^3))*sqrt(b*x^2+a)/d^8/(d*x+c)^5-1/120*(30*a^2*d^4*(C*d-3*D*c)+a*b*d^2*(65*A*d^3-191*B*c*d^2+377*C*c^2*d-623*D*c^3)+b^2*(200*A*c^2*d^3-326*B*c^3*d^2+482*C*c^4*d-668*D*c^5))*sqrt(b*x^2+a)/d^8/(d*x+c)^4-1/120*(40*a^3*d^6*D-2*a^2*b*d^4*(-44*B*d^2+173*C*c*d-447*D*c^2)-a*b^2*c*d^2*(195*A*d^3-557*B*c*d^2+1259*C*c^2*d-2421*D*c^3)-2*b^3*c^3*(100*A*d^3-237*B*c*d^2+459*C*c^2*d-786*D*c^3))*sqrt(b*x^2+a)/d^8/(a*d^2+b*c^2)/(d*x+c)^3-1/240*b*(10*a^3*d^6*(27*C*d-133*D*c)+a^2*b*d^4*(165*A*d^3-787*B*c*d^2+2809*C*c^2*d-7791*D*c^3)+2*a*b^2*c^2*d^2*(195*A*d^3-832*B*c*d^2+2464*C*c^2*d-5871*D*c^3)+4*b^3*c^4*(50*A*d^3-213*B*c*d^2+591*C*c^2*d-1314*D*c^3))*sqrt(b*x^2+a)/d^8/(a*d^2+b*c^2)^2/(d*x+c)^2-1/240*b*(560*a^4*d^8*D-2*a^3*b*d^6*(-184*B*d^2+1063*C*c*d-4417*D*c^2)-2*a*b^3*c^3*d^2*(65*A*d^3-842*B*c*d^2+3854*C*c^2*d-12201*D*c^3)-3*a^2*b^2*c*d^4*(55*A*d^3-513*B*c*d^2+2411*C*c^2*d-8189*D*c^3)-4*b^4*c^5*(10*A*d^3-147*B*c*d^2+669*C*c^2*d-2046*D*c^3))*sqrt(b*x^2+a)/d^8/(a*d^2+b*c^2)^3/(d*x+c)+1/2*b^(3/2)*(5*a*d^2*D-2*b*(-B*d^2+7*C*c*d-28*D*c^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^9-1/16*b^2*(30*a^4*d^8*(C*d-7*D*c)+8*a*b^3*c^5*d^2*(-7*B*d^2+49*C*c*d-201*D*c^2)+70*a^2*b^2*c^3*d^4*(-B*d^2+7*C*c*d-30*D*c^2)+16*b^4*c^7*(-B*d^2+7*C*c*d-28*D*c^2)+5*a^3*b*d^6*(A*d^3-7*B*c*d^2+49*C*c^2*d-231*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9/(a*d^2+b*c^2)^(7/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^8,x,13,-1/16*b^2*(16*(a*d^2+b*c^2)^4*(C*d-8*D*c)-d*(30*a^4*d^8*D-8*b^4*c^7*(C*d-8*D*c)-30*a*b^3*c^5*d^2*(C*d-8*D*c)-a^3*b*d^6*(-5*B*d^2+24*C*c*d-187*D*c^2)-a^2*b^2*c*d^4*(-5*A*d^3+41*C*c^2*d-328*D*c^3))*x)*sqrt(b*x^2+a)/d^8/(a*d^2+b*c^2)^4/(d*x+c)-1/48*b*(2*a^4*d^8*(8*C*d-19*D*c)-8*b^4*c^8*(C*d-8*D*c)-26*a*b^3*c^6*d^2*(C*d-8*D*c)-a^3*b*c*d^6*(-15*B*d^2+8*C*c*d-49*D*c^2)-3*a^2*b^2*c^2*d^4*(-5*A*d^3+9*C*c^2*d-72*D*c^3)+d*(30*a^4*d^8*D-12*b^4*c^7*(C*d-8*D*c)-5*a^3*b*d^6*(-B*d^2+8*C*c*d-51*D*c^2)-a^2*b^2*c*d^4*(-5*A*d^3+10*B*c*d^2+57*C*c^2*d-466*D*c^3)-2*a*b^3*c^3*d^2*(5*A*d^3+22*C*c^2*d-176*D*c^3))*x)*(b*x^2+a)^(3/2)/d^6/(a*d^2+b*c^2)^4/(d*x+c)^3+1/120*(6*b^3*c^6*(C*d-8*D*c)-6*a^3*d^6*(4*C*d-7*D*c)+a^2*b*c*d^4*(-25*B*d^2+8*C*c*d-39*D*c^2)+a*b^2*c^2*d^2*(-25*A*d^3+13*C*c^2*d-104*D*c^3)-5*d*(6*a^3*d^6*D-a^2*b*d^4*(-B*d^2+8*C*c*d-39*D*c^2)-a*b^2*c*d^2*(-A*d^3+4*B*c*d^2+5*C*c^2*d-44*D*c^3)-2*b^3*(2*A*c^3*d^3+C*c^5*d-8*D*c^6))*x)*(b*x^2+a)^(5/2)/d^4/(a*d^2+b*c^2)^3/(d*x+c)^5-1/7*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^7+1/6*(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*(-A*c*d^3+C*c^3*d-2*D*c^4))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^6+b^(5/2)*(C*d-8*D*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^9-1/16*b^2*(30*a^5*d^10*D-16*b^5*c^9*(C*d-8*D*c)-72*a*b^4*c^7*d^2*(C*d-8*D*c)-126*a^2*b^3*c^5*d^4*(C*d-8*D*c)-5*a^4*b*d^8*(-B*d^2+8*C*c*d-63*D*c^2)-5*a^3*b^2*c*d^6*(-A*d^3+21*C*c^2*d-168*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9/(a*d^2+b*c^2)^(9/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^9,x,10,-1/128*b^2*(128*b^5*c^11*D+576*a*b^4*c^9*d^2*D+976*a^2*b^3*c^7*d^4*D+8*a^5*d^10*(5*C*d-13*D*c)-5*a^4*b*d^8*(A*d^3-9*B*c*d^2+C*c^2*d-25*D*c^3)+8*a^3*b^2*c^2*d^6*(5*A*d^3+89*D*c^3)+d*(192*b^5*c^10*D+944*a*b^4*c^8*d^2*D+128*a^5*d^10*D-8*a^4*b*c*d^8*(5*C*d-109*D*c)-8*a^2*b^3*c^3*d^4*(5*A*d^3-231*D*c^3)+5*a^3*b^2*c*d^6*(A*d^3-9*B*c*d^2+C*c^2*d+359*D*c^3))*x)*sqrt(b*x^2+a)/d^8/(a*d^2+b*c^2)^5/(d*x+c)^2-1/192*b*(64*b^4*c^9*D+208*a*b^3*c^7*d^2*D+8*a^4*d^8*(5*C*d-13*D*c)-a^3*b*d^6*(5*A*d^3-45*B*c*d^2+5*C*c^2*d+3*D*c^3)+40*a^2*b^2*c^2*d^4*(A*d^3+5*D*c^3)+d*(112*b^4*c^8*D+64*a^4*d^8*D-8*a^3*b*c*d^6*(5*C*d-53*D*c)-40*a*b^3*c^3*d^2*(A*d^3-11*D*c^3)+a^2*b^2*c*d^4*(5*A*d^3-45*B*c*d^2+5*C*c^2*d+643*D*c^3))*x)*(b*x^2+a)^(3/2)/d^6/(a*d^2+b*c^2)^4/(d*x+c)^4-1/240*(48*b^3*c^7*D+8*a^3*d^6*(5*C*d-9*D*c)-a^2*b*d^4*(5*A*d^3-45*B*c*d^2+5*C*c^2*d-29*D*c^3)+8*a*b^2*c^2*d^2*(5*A*d^3+13*D*c^3)-d*(5*A*b^2*c*d^3*(-a*d^2+8*b*c^2)-88*b^3*c^6*D-48*a^3*d^6*D+8*a^2*b*c*d^4*(5*C*d-33*D*c)-a*b^2*c^2*d^2*(-45*B*d^2+5*C*c*d+259*D*c^2))*x)*(b*x^2+a)^(5/2)/d^4/(a*d^2+b*c^2)^3/(d*x+c)^6-1/8*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^8+1/56*(8*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-9*A*d^3+B*c*d^2+7*C*c^2*d-15*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^7+b^(5/2)*D*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^9+1/128*b^3*(128*b^5*c^11*D+704*a*b^4*c^9*d^2*D+1584*a^2*b^3*c^7*d^4*D-40*a^5*d^10*(C*d-9*D*c)-8*a^3*b^2*c^2*d^6*(5*A*d^3-231*D*c^3)+5*a^4*b*d^8*(A*d^3-9*B*c*d^2+C*c^2*d+231*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^9/(a*d^2+b*c^2)^(11/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^10,x,8,-5/128*a^2*b^2*(A*b^2*c*(-3*a*d^2+8*b*c^2)-a*(b^2*c^2*(-10*B*d+C*c)-8*a^2*d^3*D-a*b*d*(-B*d^2+10*C*c*d-3*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^6/(d*x+c)^2-5/192*a*b*(A*b^2*c*(-3*a*d^2+8*b*c^2)-a*(b^2*c^2*(-10*B*d+C*c)-8*a^2*d^3*D-a*b*d*(-B*d^2+10*C*c*d-3*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^5/(d*x+c)^4-1/48*(A*b^2*c*(-3*a*d^2+8*b*c^2)-a*(b^2*c^2*(-10*B*d+C*c)-8*a^2*d^3*D-a*b*d*(-B*d^2+10*C*c*d-3*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)^4/(d*x+c)^6-1/9*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^9+1/72*(9*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-11*A*d^3+2*B*c*d^2+7*C*c^2*d-16*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^8-1/504*(72*a^2*d^4*(C*d-3*D*c)-b^2*c^2*(-83*A*d^3+2*B*c*d^2+7*C*c^2*d+56*D*c^3)-a*b*d^2*(16*A*d^3-97*B*c*d^2+34*C*c^2*d+173*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^7-5/128*a^3*b^3*(A*b^2*c*(-3*a*d^2+8*b*c^2)-a*(b^2*c^2*(-10*B*d+C*c)-8*a^2*d^3*D-a*b*d*(-B*d^2+10*C*c*d-3*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(13/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^11,x,9,-1/256*a^2*b^3*(A*b*(3*a^2*d^4-60*a*b*c^2*d^2+80*b^2*c^4)-a*(10*b^2*c^3*(-11*B*d+C*c)+10*a^2*d^3*(C*d-11*D*c)-3*a*b*c*d*(-11*B*d^2+41*C*c*d-11*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^7/(d*x+c)^2-1/384*a*b^2*(A*b*(3*a^2*d^4-60*a*b*c^2*d^2+80*b^2*c^4)-a*(10*b^2*c^3*(-11*B*d+C*c)+10*a^2*d^3*(C*d-11*D*c)-3*a*b*c*d*(-11*B*d^2+41*C*c*d-11*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^6/(d*x+c)^4-1/480*b*(A*b*(3*a^2*d^4-60*a*b*c^2*d^2+80*b^2*c^4)-a*(10*b^2*c^3*(-11*B*d+C*c)+10*a^2*d^3*(C*d-11*D*c)-3*a*b*c*d*(-11*B*d^2+41*C*c*d-11*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)^5/(d*x+c)^6-1/10*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^10+1/90*(10*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-13*A*d^3+3*B*c*d^2+7*C*c^2*d-17*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^9-1/720*(90*a^2*d^4*(C*d-3*D*c)-2*b^2*c^2*(-58*A*d^3+3*B*c*d^2+7*C*c^2*d+28*D*c^3)-a*b*d^2*(27*A*d^3-137*B*c*d^2+67*C*c^2*d+183*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^8-1/5040*(720*a^3*d^6*D+10*a^2*b*d^4*(-16*B*d^2+113*C*c*d-75*D*c^2)-2*b^3*c^3*(-418*A*d^3+3*B*c*d^2+7*C*c^2*d+28*D*c^3)-a*b^2*c*d^2*(451*A*d^3-1121*B*c*d^2+171*C*c^2*d+239*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^4/(d*x+c)^7-1/256*a^3*b^4*(A*b*(3*a^2*d^4-60*a*b*c^2*d^2+80*b^2*c^4)-a*(10*b^2*c^3*(-11*B*d+C*c)+10*a^2*d^3*(C*d-11*D*c)-3*a*b*c*d*(-11*B*d^2+41*C*c*d-11*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(15/2),1],
[(b*x^2+a)^(5/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^12,x,10,-1/256*a^2*b^3*(5*A*b^2*c*(3*a^2*d^4-20*a*b*c^2*d^2+16*b^2*c^4)-a*(10*b^3*c^4*(-12*B*d+C*c)+10*a^3*d^5*D+a^2*b*d^3*(-3*B*d^2+36*C*c*d-149*D*c^2)-a*b^2*c^2*d*(-72*B*d^2+149*C*c*d-36*D*c^2)))*(-b*c*x+a*d)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^8/(d*x+c)^2-1/384*a*b^2*(5*A*b^2*c*(3*a^2*d^4-20*a*b*c^2*d^2+16*b^2*c^4)-a*(10*b^3*c^4*(-12*B*d+C*c)+10*a^3*d^5*D+a^2*b*d^3*(-3*B*d^2+36*C*c*d-149*D*c^2)-a*b^2*c^2*d*(-72*B*d^2+149*C*c*d-36*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(3/2)/(a*d^2+b*c^2)^7/(d*x+c)^4-1/480*b*(5*A*b^2*c*(3*a^2*d^4-20*a*b*c^2*d^2+16*b^2*c^4)-a*(10*b^3*c^4*(-12*B*d+C*c)+10*a^3*d^5*D+a^2*b*d^3*(-3*B*d^2+36*C*c*d-149*D*c^2)-a*b^2*c^2*d*(-72*B*d^2+149*C*c*d-36*D*c^2)))*(-b*c*x+a*d)*(b*x^2+a)^(5/2)/(a*d^2+b*c^2)^6/(d*x+c)^6-1/11*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)/(d*x+c)^11+1/110*(11*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-15*A*d^3+4*B*c*d^2+7*C*c^2*d-18*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^2/(d*x+c)^10-1/990*(110*a^2*d^4*(C*d-3*D*c)-b^2*c^2*(-155*A*d^3+12*B*c*d^2+21*C*c^2*d+56*D*c^3)-a*b*d^2*(40*A*d^3-183*B*c*d^2+106*C*c^2*d+191*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^3/(d*x+c)^9-1/7920*(990*a^3*d^6*D+11*a^2*b*d^4*(-27*B*d^2+164*C*c*d-141*D*c^2)-2*b^3*c^3*(-650*A*d^3+12*B*c*d^2+21*C*c^2*d+56*D*c^3)-a*b^2*c*d^2*(845*A*d^3-1824*B*c*d^2+383*C*c^2*d+508*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^4/(d*x+c)^8+1/55440*b*(110*a^3*d^6*(16*C*d-129*D*c)-a^2*b*d^4*(640*A*d^3-5601*B*c*d^2+16172*C*c^2*d-5623*D*c^3)+2*b^3*c^4*(-4610*A*d^3+12*B*c*d^2+21*C*c^2*d+56*D*c^3)+5*a*b^2*c^2*d^2*(1889*A*d^3-2736*B*c*d^2+283*C*c^2*d+124*D*c^3))*(b*x^2+a)^(7/2)/d^2/(a*d^2+b*c^2)^5/(d*x+c)^7-1/256*a^3*b^4*(5*A*b^2*c*(3*a^2*d^4-20*a*b*c^2*d^2+16*b^2*c^4)-a*(10*b^3*c^4*(-12*B*d+C*c)+10*a^3*d^5*D+a^2*b*d^3*(-3*B*d^2+36*C*c*d-149*D*c^2)-a*b^2*c^2*d*(-72*B*d^2+149*C*c*d-36*D*c^2)))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(17/2),1],
[(d*x+c)^3*(D*x^3+C*x^2+B*x+A)/sqrt(b*x^2+a),x,9,(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*sqrt(b*x^2+a)/b^3+1/16*(8*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-6*a*b*d*(B*d^2+3*C*c*d+3*D*c^2))*x*sqrt(b*x^2+a)/b^3-1/24*d*(5*a*d^2*D-6*b*(B*d^2+3*C*c*d+3*D*c^2))*x^3*sqrt(b*x^2+a)/b^2+1/6*d^3*D*x^5*sqrt(b*x^2+a)/b-1/3*(2*a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*(b*x^2+a)^(3/2)/b^3+1/5*d^2*(C*d+3*D*c)*(b*x^2+a)^(5/2)/b^3+1/16*(16*A*b^3*c^3-a*(8*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+5*a^2*d^3*D-6*a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x+c)^2*(D*x^3+C*x^2+B*x+A)/sqrt(b*x^2+a),x,8,(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))*sqrt(b*x^2+a)/b^3+1/8*(4*b*(A*d^2+2*B*c*d+C*c^2)-3*a*d*(C*d+2*D*c))*x*sqrt(b*x^2+a)/b^2+1/4*d*(C*d+2*D*c)*x^3*sqrt(b*x^2+a)/b-1/3*(2*a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))*(b*x^2+a)^(3/2)/b^3+1/5*d^2*D*(b*x^2+a)^(5/2)/b^3+1/8*(4*A*b*(-a*d^2+2*b*c^2)-a*(4*b*c*(2*B*d+C*c)-3*a*d*(C*d+2*D*c)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)*(D*x^3+C*x^2+B*x+A)/sqrt(b*x^2+a),x,8,(A*b*d+B*b*c-C*a*d-D*a*c)*sqrt(b*x^2+a)/b^2+1/8*(4*b*(B*d+C*c)-3*a*d*D)*x*sqrt(b*x^2+a)/b^2+1/4*d*D*x^3*sqrt(b*x^2+a)/b+1/3*(C*d+D*c)*(b*x^2+a)^(3/2)/b^2+1/8*(8*A*b^2*c-a*(4*b*(B*d+C*c)-3*a*d*D))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(D*x^3+C*x^2+B*x+A)/sqrt(b*x^2+a),x,7,(B*b-D*a)*sqrt(b*x^2+a)/b^2+1/2*C*x*sqrt(b*x^2+a)/b+1/3*D*(b*x^2+a)^(3/2)/b^2+1/2*(2*A*b-C*a)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)/sqrt(b*x^2+a),x,7,(C*d-D*c)*sqrt(b*x^2+a)/b/d^2+1/2*D*x*sqrt(b*x^2+a)/b/d-1/2*(a*d^2*D+2*b*(-B*d^2+C*c*d-D*c^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/d^3-(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^3/sqrt(a*d^2+b*c^2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^2/sqrt(b*x^2+a),x,7,D*sqrt(b*x^2+a)/b/d^2-(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^2/(a*d^2+b*c^2)/(d*x+c)+(C*d-2*D*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/d^3+(a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*(-A*c*d^3+C*c^3*d-2*D*c^4))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^3/(a*d^2+b*c^2)^(3/2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^3/sqrt(b*x^2+a),x,7,-1/2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/d^2/(a*d^2+b*c^2)/(d*x+c)^2+1/2*(2*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)+b*c*(-3*A*d^3+B*c*d^2+C*c^2*d-3*D*c^3))*sqrt(b*x^2+a)/d^2/(a*d^2+b*c^2)^2/(d*x+c)+D*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/d^3-1/2*(A*b*d^3*(-a*d^2+2*b*c^2)-2*b^2*c^5*D+2*a^2*d^4*(C*d-3*D*c)-a*b*c*d^2*(-3*B*d^2+C*c*d+5*D*c^2))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d^3/(a*d^2+b*c^2)^(5/2),1],
[(d*x+c)^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^(3/2),x,9,-(b^2*c^2*(3*A*d+B*c)+a^2*d^2*(C*d+3*D*c)-a*b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))/b^3/sqrt(b*x^2+a)+(A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(3*B*d+C*c)+a^2*d^3*D-a*b*d*(B*d^2+3*C*c*d+3*D*c^2)))*x/a/b^3/sqrt(b*x^2+a)-(2*a*d^2*(C*d+3*D*c)-b*(A*d^3+3*B*c*d^2+3*C*c^2*d+D*c^3))*sqrt(b*x^2+a)/b^3-1/8*d*(7*a*d^2*D-4*b*(B*d^2+3*C*c*d+3*D*c^2))*x*sqrt(b*x^2+a)/b^3+1/4*d^3*D*x^3*sqrt(b*x^2+a)/b^2+1/3*d^2*(C*d+3*D*c)*(b*x^2+a)^(3/2)/b^3+1/8*(8*b^2*c*(3*A*d^2+3*B*c*d+C*c^2)+15*a^2*d^3*D-12*a*b*d*(B*d^2+3*C*c*d+3*D*c^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x+c)^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^(3/2),x,8,-(b^2*c*(2*A*d+B*c)+a^2*d^2*D-a*b*(B*d^2+2*C*c*d+D*c^2))/b^3/sqrt(b*x^2+a)+(A*b*(-a*d^2+b*c^2)-a*(b*c*(2*B*d+C*c)-a*d*(C*d+2*D*c)))*x/a/b^2/sqrt(b*x^2+a)-(2*a*d^2*D-b*(B*d^2+2*C*c*d+D*c^2))*sqrt(b*x^2+a)/b^3+1/2*d*(C*d+2*D*c)*x*sqrt(b*x^2+a)/b^2+1/3*d^2*D*(b*x^2+a)^(3/2)/b^3+1/2*(2*b*(A*d^2+2*B*c*d+C*c^2)-3*a*d*(C*d+2*D*c))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x+c)*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^(3/2),x,8,-(A*b*d+B*b*c-C*a*d-D*a*c)/b^2/sqrt(b*x^2+a)+(A*b^2*c-a*(b*(B*d+C*c)-a*d*D))*x/a/b^2/sqrt(b*x^2+a)+(C*d+D*c)*sqrt(b*x^2+a)/b^2+1/2*d*D*x*sqrt(b*x^2+a)/b^2+1/2*(2*b*(B*d+C*c)-3*a*d*D)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^(3/2),x,7,-(B*b-D*a)/b^2/sqrt(b*x^2+a)+(A*b-C*a)*x/a/b/sqrt(b*x^2+a)+D*sqrt(b*x^2+a)/b^2+C*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)/(b*x^2+a)^(3/2),x,6,-(a*(-A*b*d+B*b*c+C*a*d-D*a*c)-(A*b^2*c-a*(-B*b*d+C*b*c+D*a*d))*x)/a/b/(a*d^2+b*c^2)/sqrt(b*x^2+a)+D*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/d-(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/d/(a*d^2+b*c^2)^(3/2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^2/(b*x^2+a)^(3/2),x,4,-(a*(b^2*c*(-2*A*d+B*c)+a^2*d^2*D+a*b*(-B*d^2+2*C*c*d-D*c^2))-b*(A*b*(-a*d^2+b*c^2)-a*(b*c*(-2*B*d+C*c)-a*d*(C*d-2*D*c)))*x)/a/b/(a*d^2+b*c^2)^2/sqrt(b*x^2+a)-(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^2/(d*x+c)-(b*c*(3*A*d^2-2*B*c*d+C*c^2)-a*d*(-B*d^2+2*C*c*d-3*D*c^2))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(5/2),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^3/(b*x^2+a)^(3/2),x,5,-(a*(b^2*c^2*(-3*A*d+B*c)-a^2*d^2*(C*d-3*D*c)+a*b*(A*d^3-3*B*c*d^2+3*C*c^2*d-D*c^3))-(A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(-3*B*d+C*c)-a^2*d^3*D-a*b*d*(-B*d^2+3*C*c*d-3*D*c^2)))*x)/a/(a*d^2+b*c^2)^3/sqrt(b*x^2+a)-1/2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(b*x^2+a)/(a*d^2+b*c^2)^2/(d*x+c)^2+1/2*(2*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(7*A*d^3-5*B*c*d^2+3*C*c^2*d-D*c^3))*sqrt(b*x^2+a)/(a*d^2+b*c^2)^3/(d*x+c)-1/2*(2*b^2*c^2*(6*A*d^2-3*B*c*d+C*c^2)+2*a^2*d^3*(C*d-3*D*c)-a*b*d*(3*A*d^3-9*B*c*d^2+11*C*c^2*d-9*D*c^3))*arctanh((-b*c*x+a*d)/sqrt(a*d^2+b*c^2)/sqrt(b*x^2+a))/(a*d^2+b*c^2)^(7/2),1],
[(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^(5/2),x,6,-1/3*(B*b-D*a)/b^2/(b*x^2+a)^(3/2)+1/3*(A*b-C*a)*x/a/b/(b*x^2+a)^(3/2)-D/b^2/sqrt(b*x^2+a)+1/3*(2*A*b+C*a)*x/a^2/b/sqrt(b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^(7/2),x,7,-1/5*(B*b-D*a)/b^2/(b*x^2+a)^(5/2)+1/5*(A*b-C*a)*x/a/b/(b*x^2+a)^(5/2)-1/3*D/b^2/(b*x^2+a)^(3/2)+1/15*(4*A*b+C*a)*x/a^2/b/(b*x^2+a)^(3/2)+2/15*(4*A*b+C*a)*x/a^3/b/sqrt(b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^(9/2),x,8,-1/7*(B*b-D*a)/b^2/(b*x^2+a)^(7/2)+1/7*(A*b-C*a)*x/a/b/(b*x^2+a)^(7/2)-1/5*D/b^2/(b*x^2+a)^(5/2)+1/35*(6*A*b+C*a)*x/a^2/b/(b*x^2+a)^(5/2)+4/105*(6*A*b+C*a)*x/a^3/b/(b*x^2+a)^(3/2)+8/105*(6*A*b+C*a)*x/a^4/b/sqrt(b*x^2+a),1],
[(1+2*x)^3*(4*x^2+3*x+1)/sqrt(3*x^2+2),x,7,-199/27*sqrt(3*x^2+2)-1/3*x*sqrt(3*x^2+2)+6*x^3*sqrt(3*x^2+2)+76/81*(3*x^2+2)^(3/2)+32/135*(3*x^2+2)^(5/2)+5/3*arcsinh(sqrt(3/2)*x)/sqrt(3),1],
[(1+2*x)^2*(4*x^2+3*x+1)/sqrt(3*x^2+2),x,7,-35/9*sqrt(3*x^2+2)+2*x*sqrt(3*x^2+2)+4/3*x^3*sqrt(3*x^2+2)+28/27*(3*x^2+2)^(3/2)-sqrt(3)*arcsinh(sqrt(3/2)*x),1],
[(1+2*x)*(4*x^2+3*x+1)/sqrt(3*x^2+2),x,6,-1/9*sqrt(3*x^2+2)+5/3*x*sqrt(3*x^2+2)+8/27*(3*x^2+2)^(3/2)-7/3*arcsinh(sqrt(3/2)*x)/sqrt(3),1],
[(4*x^2+3*x+1)/(1+2*x)/sqrt(3*x^2+2),x,5,2/3*sqrt(3*x^2+2)+1/2*arcsinh(sqrt(3/2)*x)/sqrt(3)-1/2*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[(4*x^2+3*x+1)/(1+2*x)^2/sqrt(3*x^2+2),x,5,-1/11*sqrt(3*x^2+2)/(1+2*x)+arcsinh(sqrt(3/2)*x)/sqrt(3)+4/11*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[(4*x^2+3*x+1)/(1+2*x)^3/sqrt(3*x^2+2),x,4,-1/22*sqrt(3*x^2+2)/(1+2*x)^2+13*sqrt(3*x^2+2)/(242+484*x)-103/121*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[(1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x,7,199/27/sqrt(3*x^2+2)+31/6*x/sqrt(3*x^2+2)+76/27*sqrt(3*x^2+2)+4*x*sqrt(3*x^2+2)+32/81*(3*x^2+2)^(3/2)-38/3*arcsinh(sqrt(3/2)*x)/sqrt(3),1],
[(1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x,7,35/9/sqrt(3*x^2+2)-47/18*x/sqrt(3*x^2+2)+28/9*sqrt(3*x^2+2)+8/9*x*sqrt(3*x^2+2)+4/3*arcsinh(sqrt(3/2)*x)/sqrt(3),1],
[(1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x,6,1/9/sqrt(3*x^2+2)-17/6*x/sqrt(3*x^2+2)+8/9*sqrt(3*x^2+2)+10/3*arcsinh(sqrt(3/2)*x)/sqrt(3),1],
[(4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(3/2),x,4,1/66*(-38+21*x)/sqrt(3*x^2+2)-2/11*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[(4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(3/2),x,4,1/242*(-10+97*x)/sqrt(3*x^2+2)-4*sqrt(3*x^2+2)/(121+242*x)+4/121*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[(4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(3/2),x,5,1/2662*(358+351*x)/sqrt(3*x^2+2)-2/121*sqrt(3*x^2+2)/(1+2*x)^2+2*sqrt(3*x^2+2)/(1331+2662*x)-322/1331*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[(1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x,7,199/81/(3*x^2+2)^(3/2)+31/18*x/(3*x^2+2)^(3/2)-76/27/sqrt(3*x^2+2)-155/18*x/sqrt(3*x^2+2)+32/27*sqrt(3*x^2+2)+8*arcsinh(sqrt(3/2)*x)/sqrt(3),1],
[(1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x,7,35/27/(3*x^2+2)^(3/2)-47/54*x/(3*x^2+2)^(3/2)-28/9/sqrt(3*x^2+2)-59/54*x/sqrt(3*x^2+2)+16/9*arcsinh(sqrt(3/2)*x)/sqrt(3),1],
[(1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x,6,1/27/(3*x^2+2)^(3/2)-17/18*x/(3*x^2+2)^(3/2)-8/9/sqrt(3*x^2+2)+13/18*x/sqrt(3*x^2+2),1],
[(4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(5/2),x,5,1/198*(-38+21*x)/(3*x^2+2)^(3/2)+1/726*(24+95*x)/sqrt(3*x^2+2)-8/121*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[(4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(5/2),x,5,1/726*(-10+97*x)/(3*x^2+2)^(3/2)+1/7986*(24+887*x)/sqrt(3*x^2+2)-16*sqrt(3*x^2+2)/(1331+2662*x)-32/1331*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[(4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(5/2),x,6,1/7986*(358+351*x)/(3*x^2+2)^(3/2)+1/29282*(1216+2133*x)/sqrt(3*x^2+2)-8/1331*sqrt(3*x^2+2)/(1+2*x)^2-8*sqrt(3*x^2+2)/(1331+2662*x)-1216/14641*arctanh((4-3*x)/sqrt(11)/sqrt(3*x^2+2))/sqrt(11),1],
[sqrt(d*x+c)*sqrt(-b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,14,2/3465*(75*a^2*d^4*D-3*a*b*d^2*(-55*B*d^2+11*C*c*d-2*D*c^2)+b^2*c*(231*A*d^3-132*B*c*d^2+88*C*c^2*d-64*D*c^3))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b^2/d^4+2/1155*(a*d^2*(77*C*d+D*c)-b*(-231*A*d^3-33*B*c*d^2+22*C*c^2*d-16*D*c^3))*x*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^3-2/231*(15*a*d^2*D-b*(-33*B*d^2+22*C*c*d-16*D*c^2))*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/b^2/d^2-2/99*(11*C*d-17*D*c)*(d*x+c)^(3/2)*(-b*x^2+a)^(3/2)/b/d^2-2/11*D*(d*x+c)^(5/2)*(-b*x^2+a)^(3/2)/b/d^2-4/3465*sqrt(a)*(3*a^2*d^4*(77*C*d+26*D*c)+b^2*c^2*(231*A*d^3-132*B*c*d^2+88*C*c^2*d-64*D*c^3)-3*a*b*d^2*(-231*A*d^3-88*B*c*d^2+33*C*c^2*d-18*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^5/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+4/3465*sqrt(a)*(-a*d^2+b*c^2)*(75*a^2*d^4*D-3*a*b*d^2*(-55*B*d^2+11*C*c*d-2*D*c^2)+b^2*c*(231*A*d^3-132*B*c*d^2+88*C*c^2*d-64*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(5/2)/d^5/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(-b*x^2+a)*(D*x^3+C*x^2+B*x+A)/sqrt(d*x+c),x,13,2/315*(3*a*d^2*(5*C*d-6*D*c)+b*(105*A*d^3-84*B*c*d^2+72*C*c^2*d-64*D*c^3))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^4+2/105*(7*a*d^2*D-b*(-21*B*d^2+18*C*c*d-16*D*c^2))*x*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^3-2/21*(3*C*d-5*D*c)*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/b/d^2-2/9*D*(d*x+c)^(3/2)*(-b*x^2+a)^(3/2)/b/d^2-4/315*sqrt(a)*(21*a^2*d^4*D-3*a*b*d^2*(-21*B*d^2+13*C*c*d-10*D*c^2)+b^2*c*(105*A*d^3-84*B*c*d^2+72*C*c^2*d-64*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^5/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+4/315*sqrt(a)*(-a*d^2+b*c^2)*(3*a*d^2*(5*C*d-6*D*c)+b*(105*A*d^3-84*B*c*d^2+72*C*c^2*d-64*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^5/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(-b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x,13,-2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^4/sqrt(d*x+c)-2/105*(10*a*d^2*D+b*(-35*B*d^2+84*C*c*d-141*D*c^2))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^4+2/35*(7*C*d-23*D*c)*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d^4+2/7*D*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/d^4-4/105*sqrt(a)*(a*d^2*(21*C*d-34*D*c)-b*(105*A*d^3-140*B*c*d^2+168*C*c^2*d-192*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^5/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-4/105*sqrt(a)*(5*a^2*d^4*D-a*b*d^2*(-35*B*d^2+63*C*c*d-82*D*c^2)+b^2*c*(105*A*d^3-140*B*c*d^2+168*C*c^2*d-192*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^5/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(-b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x,13,-2/3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^4/(d*x+c)^(3/2)-2/3*(3*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(2*A*d^3-5*B*c*d^2+8*C*c^2*d-11*D*c^3))*sqrt(-b*x^2+a)/d^4/(-a*d^2+b*c^2)/sqrt(d*x+c)+2/15*(5*C*d-17*D*c)*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^4+2/5*D*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d^4+4/15*sqrt(a)*(3*a^2*d^4*D+a*b*d^2*(-15*B*d^2+35*C*c*d-62*D*c^2)-b^2*c*(5*A*d^3-20*B*c*d^2+40*C*c^2*d-64*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^5/(-a*d^2+b*c^2)/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-4/15*sqrt(a)*(a*d^2*(5*C*d-14*D*c)-b*(5*A*d^3-20*B*c*d^2+40*C*c^2*d-64*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^5/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(-b*x^2+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(7/2),x,13,-2/5*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^4/(d*x+c)^(5/2)-2/15*(5*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(2*A*d^3-7*B*c*d^2+12*C*c^2*d-17*D*c^3))*sqrt(-b*x^2+a)/d^4/(-a*d^2+b*c^2)/(d*x+c)^(3/2)-2/15*(15*a^2*d^4*(C*d-3*D*c)+b^2*c^2*(-2*A*d^3-8*B*c*d^2+33*C*c^2*d-73*D*c^3)-2*a*b*d^2*(3*A*d^3-8*B*c*d^2+28*C*c^2*d-63*D*c^3))*sqrt(-b*x^2+a)/d^4/(-a*d^2+b*c^2)^2/sqrt(d*x+c)+2/3*D*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^4+4/15*sqrt(a)*sqrt(b)*(5*a^2*d^4*(3*C*d-10*D*c)-a*b*d^2*(3*A*d^3-8*B*c*d^2+43*C*c^2*d-118*D*c^3)+b^2*c^2*(-A*d^3-4*B*c*d^2+24*C*c^2*d-64*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^5/(-a*d^2+b*c^2)^2/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+4/15*sqrt(a)*(5*a^2*d^4*D+5*a*b*d^2*(-B*d^2+5*C*c*d-14*D*c^2)-b^2*c*(-A*d^3-4*B*c*d^2+24*C*c^2*d-64*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^5/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)*(-b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A),x,16,4/45045*(195*a^3*d^6*D-9*a^2*b*d^4*(-65*B*d^2+6*C*c*d+3*D*c^2)+3*a*b^2*c*d^2*(572*A*d^3-299*B*c*d^2+186*C*c^2*d-128*D*c^3)-4*b^3*c^3*(143*A*d^3-104*B*c*d^2+80*C*c^2*d-64*D*c^3))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b^2/d^6+4/15015*(3*a^2*d^4*(77*C*d+6*D*c)-a*b*d^2*(-1001*A*d^3-208*B*c*d^2+127*C*c^2*d-86*D*c^3)+b^2*c^2*(143*A*d^3-104*B*c*d^2+80*C*c^2*d-64*D*c^3))*x*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^5+2/9009*(39*a^2*d^4*D-3*a*b*d^2*(-39*B*d^2+19*C*c*d-10*D*c^2)+b^2*c*(143*A*d^3-104*B*c*d^2+80*C*c^2*d-64*D*c^3))*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/b^2/d^4+2/1287*(3*a*d^2*(11*C*d-D*c)-b*(-143*A*d^3-13*B*c*d^2+10*C*c^2*d-8*D*c^3))*x*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/b/d^3-2/429*(13*a*D-3*b*(-13*B*d^2+10*C*c*d-8*D*c^2)/d^2)*sqrt(d*x+c)*(-b*x^2+a)^(5/2)/b^2-2/39*(3*C*d-5*D*c)*(d*x+c)^(3/2)*(-b*x^2+a)^(5/2)/b/d^2-2/15*D*(d*x+c)^(5/2)*(-b*x^2+a)^(5/2)/b/d^2-8/45045*sqrt(a)*(3*a^3*d^6*(231*C*d+83*D*c)+3*a*b^2*c^2*d^2*(715*A*d^3-403*B*c*d^2+266*C*c^2*d-192*D*c^3)-3*a^2*b*d^4*(-1001*A*d^3-403*B*c*d^2+145*C*c^2*d-77*D*c^3)-4*b^3*c^4*(143*A*d^3-104*B*c*d^2+80*C*c^2*d-64*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^7/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+8/45045*sqrt(a)*(-a*d^2+b*c^2)*(195*a^3*d^6*D-9*a^2*b*d^4*(-65*B*d^2+6*C*c*d+3*D*c^2)+3*a*b^2*c*d^2*(572*A*d^3-299*B*c*d^2+186*C*c^2*d-128*D*c^3)-4*b^3*c^3*(143*A*d^3-104*B*c*d^2+80*C*c^2*d-64*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(5/2)/d^7/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/sqrt(d*x+c),x,15,4/45045*(9*a^2*d^4*(65*C*d-71*D*c)+3*a*b*d^2*(2145*A*d^3-1573*B*c*d^2+1274*C*c^2*d-1088*D*c^3)-4*b^2*c^2*(1287*A*d^3-1144*B*c*d^2+1040*C*c^2*d-960*D*c^3))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^6+4/15015*(231*a^2*d^4*D-a*b*d^2*(-1001*B*d^2+793*C*c*d-666*D*c^2)+b^2*c*(1287*A*d^3-1144*B*c*d^2+1040*C*c^2*d-960*D*c^3))*x*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^5+2/9009*(3*a*d^2*(39*C*d-58*D*c)+b*(1287*A*d^3-1144*B*c*d^2+1040*C*c^2*d-960*D*c^3))*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/b/d^4+2/1287*(33*a*d^2*D-b*(-143*B*d^2+130*C*c*d-120*D*c^2))*x*sqrt(d*x+c)*(-b*x^2+a)^(3/2)/b/d^3-2/143*(13*C*d-23*D*c)*sqrt(d*x+c)*(-b*x^2+a)^(5/2)/b/d^2-2/13*D*(d*x+c)^(3/2)*(-b*x^2+a)^(5/2)/b/d^2-8/45045*sqrt(a)*(693*a^3*d^6*D-3*a^2*b*d^4*(-1001*B*d^2+598*C*c*d-453*D*c^2)+3*a*b^2*c*d^2*(3432*A*d^3-2717*B*c*d^2+2314*C*c^2*d-2048*D*c^3)-4*b^3*c^3*(1287*A*d^3-1144*B*c*d^2+1040*C*c^2*d-960*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^7/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+8/45045*sqrt(a)*(-a*d^2+b*c^2)*(9*a^2*d^4*(65*C*d-71*D*c)+3*a*b*d^2*(2145*A*d^3-1573*B*c*d^2+1274*C*c^2*d-1088*D*c^3)-4*b^2*c^2*(1287*A*d^3-1144*B*c*d^2+1040*C*c^2*d-960*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^7/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x,15,2*(-a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^6/sqrt(d*x+c)-2/3465*(180*a^2*d^4*D+3*a*b*d^2*(-495*B*d^2+1166*C*c*d-1929*D*c^2)-b^2*c*(2772*A*d^3-4653*B*c*d^2+6710*C*c^2*d-8895*D*c^3))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^6+2/3465*(a*d^2*(847*C*d-2733*D*c)-b*(693*A*d^3-2277*B*c*d^2+4840*C*c^2*d-8430*D*c^3))*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d^6+2/693*(117*a*d^2*D+b*(-99*B*d^2+418*C*c*d-1086*D*c^2))*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/d^6-2/99*b*(11*C*d-57*D*c)*(d*x+c)^(7/2)*sqrt(-b*x^2+a)/d^6-2/11*b*D*(d*x+c)^(9/2)*sqrt(-b*x^2+a)/d^6-8/3465*sqrt(a)*(3*a^2*d^4*(77*C*d-123*D*c)-3*a*b*d^2*(693*A*d^3-957*B*c*d^2+1166*C*c^2*d-1344*D*c^3)+4*b^2*c^2*(693*A*d^3-792*B*c*d^2+880*C*c^2*d-960*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^7/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+8/3465*sqrt(a)*(-a*d^2+b*c^2)*(45*a^2*d^4*D-3*a*b*d^2*(-165*B*d^2+286*C*c*d-384*D*c^2)+4*b^2*c*(693*A*d^3-792*B*c*d^2+880*C*c^2*d-960*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^7/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x,15,2/3*(-a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^6/(d*x+c)^(3/2)+2/3*(3*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(8*A*d^3-11*B*c*d^2+14*C*c^2*d-17*D*c^3))*sqrt(-b*x^2+a)/d^6/sqrt(d*x+c)+2/315*(3*a*d^2*(45*C*d-151*D*c)-b*(105*A*d^3-357*B*c*d^2+780*C*c^2*d-1390*D*c^3))*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^6+2/315*(77*a*d^2*D+b*(-63*B*d^2+270*C*c*d-710*D*c^2))*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d^6-2/63*b*(9*C*d-47*D*c)*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/d^6-2/9*b*D*(d*x+c)^(7/2)*sqrt(-b*x^2+a)/d^6-8/315*sqrt(a)*(21*a^2*d^4*D+3*a*b*d^2*(-63*B*d^2+150*C*c*d-256*D*c^2)-4*b^2*c*(105*A*d^3-168*B*c*d^2+240*C*c^2*d-320*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^7/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-8/315*sqrt(a)*(3*a^2*d^4*(15*C*d-41*D*c)-a*b*d^2*(105*A*d^3-357*B*c*d^2+690*C*c^2*d-1088*D*c^3)+4*b^2*c^2*(105*A*d^3-168*B*c*d^2+240*C*c^2*d-320*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^7/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(7/2),x,15,2/5*(-a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^6/(d*x+c)^(5/2)+2/15*(5*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(12*A*d^3-17*B*c*d^2+22*C*c^2*d-27*D*c^3))*sqrt(-b*x^2+a)/d^6/(d*x+c)^(3/2)+2/15*(15*a^2*d^4*(C*d-3*D*c)-a*b*d^2*(21*A*d^3-61*B*c*d^2+131*C*c^2*d-231*D*c^3)+b^2*c^2*(33*A*d^3-73*B*c*d^2+128*C*c^2*d-198*D*c^3))*sqrt(-b*x^2+a)/d^6/(-a*d^2+b*c^2)/sqrt(d*x+c)+2/105*(45*a*d^2*D+b*(-35*B*d^2+154*C*c*d-414*D*c^2))*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^6-2/35*b*(7*C*d-37*D*c)*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d^6-2/7*b*D*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/d^6-8/105*sqrt(a)*sqrt(b)*(3*a^2*d^4*(21*C*d-71*D*c)-a*b*d^2*(63*A*d^3-203*B*c*d^2+490*C*c^2*d-960*D*c^3)+4*b^2*c^2*(21*A*d^3-56*B*c*d^2+112*C*c^2*d-192*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^7/(-a*d^2+b*c^2)/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-8/105*sqrt(a)*(15*a^2*d^4*D+a*b*d^2*(-35*B*d^2+154*C*c*d-384*D*c^2)-4*b^2*c*(21*A*d^3-56*B*c*d^2+112*C*c^2*d-192*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^7/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(-b*x^2+a)^(3/2)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(9/2),x,15,2/7*(-a*d^2+b*c^2)*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^6/(d*x+c)^(7/2)+2/35*(7*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(16*A*d^3-23*B*c*d^2+30*C*c^2*d-37*D*c^3))*sqrt(-b*x^2+a)/d^6/(d*x+c)^(5/2)+2/105*(35*a^2*d^4*(C*d-3*D*c)-a*b*d^2*(45*A*d^3-129*B*c*d^2+283*C*c^2*d-507*D*c^3)+b^2*c^2*(57*A*d^3-141*B*c*d^2+260*C*c^2*d-414*D*c^3))*sqrt(-b*x^2+a)/d^6/(-a*d^2+b*c^2)/(d*x+c)^(3/2)-2/105*(105*a^3*d^6*D+7*a^2*b*d^4*(-21*B*d^2+82*C*c*d-228*D*c^2)-a*b^2*c*d^2*(96*A*d^3-474*B*c*d^2+1412*C*c^2*d-3225*D*c^3)+b^3*c^3*(48*A*d^3-279*B*c*d^2+790*C*c^2*d-1686*D*c^3))*sqrt(-b*x^2+a)/d^6/(-a*d^2+b*c^2)^2/sqrt(d*x+c)-2/15*b*(5*C*d-27*D*c)*sqrt(d*x+c)*sqrt(-b*x^2+a)/d^6-2/5*b*D*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/d^6+8/105*sqrt(a)*sqrt(b)*(63*a^3*d^6*D+7*a^2*b*d^4*(-9*B*d^2+38*C*c*d-117*D*c^2)-a*b^2*c*d^2*(24*A*d^3-171*B*c*d^2+598*C*c^2*d-1536*D*c^3)+4*b^3*c^3*(3*A*d^3-24*B*c*d^2+80*C*c^2*d-192*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^7/(-a*d^2+b*c^2)^2/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-8/105*sqrt(a)*sqrt(b)*(7*a^2*d^4*(5*C*d-27*D*c)-a*b*d^2*(15*A*d^3-99*B*c*d^2+358*C*c^2*d-960*D*c^3)+4*b^2*c^2*(3*A*d^3-24*B*c*d^2+80*C*c^2*d-192*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^7/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(5/2)*(D*x^3+C*x^2+B*x+A)/sqrt(-b*x^2+a),x,14,-2/3465*(675*a^2*d^4*D+3*a*b*d^2*(275*B*d^2+418*C*c*d+95*D*c^2)-b^2*c*(-1848*A*d^3-495*B*c*d^2+110*C*c^2*d-40*D*c^3))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b^3/d^2-2/3465*(a*d^2*(539*C*d+335*D*c)-b*(-693*A*d^3-495*B*c*d^2+110*C*c^2*d-40*D*c^3))*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/b^2/d^2-2/693*(81*a*d^2*D-b*(-99*B*d^2+22*C*c*d-8*D*c^2))*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/b^2/d^2-2/99*(11*C*d-13*D*c)*(d*x+c)^(7/2)*sqrt(-b*x^2+a)/b/d^2-2/11*D*(d*x+c)^(9/2)*sqrt(-b*x^2+a)/b/d^2-2/3465*sqrt(a)*(3*a^2*d^4*(539*C*d+1235*D*c)-b^2*c^2*(-5313*A*d^3-495*B*c*d^2+110*C*c^2*d-40*D*c^3)+3*a*b*d^2*(693*A*d^3+1595*B*c*d^2+1023*C*c^2*d+85*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(5/2)/d^3/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+2/3465*sqrt(a)*(-a*d^2+b*c^2)*(675*a^2*d^4*D+3*a*b*d^2*(275*B*d^2+418*C*c*d+95*D*c^2)-b^2*c*(-1848*A*d^3-495*B*c*d^2+110*C*c^2*d-40*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(7/2)/d^3/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(3/2)*(D*x^3+C*x^2+B*x+A)/sqrt(-b*x^2+a),x,13,-2/315*(3*a*d^2*(25*C*d+13*D*c)-b*(-105*A*d^3-63*B*c*d^2+18*C*c^2*d-8*D*c^3))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b^2/d^2-2/315*(49*a*D+b*(63*B-2*c*(9*C*d-4*D*c)/d^2))*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/b^2-2/63*(9*C*d-11*D*c)*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/b/d^2-2/9*D*(d*x+c)^(7/2)*sqrt(-b*x^2+a)/b/d^2-2/315*sqrt(a)*(147*a^2*d^4*D+3*a*b*d^2*(63*B*d^2+82*C*c*d+11*D*c^2)-b^2*c*(-420*A*d^3-63*B*c*d^2+18*C*c^2*d-8*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(5/2)/d^3/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+2/315*sqrt(a)*(-a*d^2+b*c^2)*(3*a*d^2*(25*C*d+13*D*c)-b*(-105*A*d^3-63*B*c*d^2+18*C*c^2*d-8*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(5/2)/d^3/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)*(D*x^3+C*x^2+B*x+A)/sqrt(-b*x^2+a),x,12,-2/105*(25*a*D+b*(35*B-2*c*(7*C*d-4*D*c)/d^2))*sqrt(d*x+c)*sqrt(-b*x^2+a)/b^2-2/35*(7*C*d-9*D*c)*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/b/d^2-2/7*D*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/b/d^2-2/105*sqrt(a)*(a*d^2*(63*C*d+19*D*c)-b*(-105*A*d^3-35*B*c*d^2+14*C*c^2*d-8*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^3/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+2/105*sqrt(a)*(-a*d^2+b*c^2)*(25*a*d^2*D-b*(-35*B*d^2+14*C*c*d-8*D*c^2))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(5/2)/d^3/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/sqrt(d*x+c)/sqrt(-b*x^2+a),x,11,-2/15*(5*C*d-7*D*c)*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^2-2/5*D*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/b/d^2-2/15*sqrt(a)*(9*a*d^2*D-b*(-15*B*d^2+10*C*c*d-8*D*c^2))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^3/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-2/15*sqrt(a)*(a*d^2*(5*C*d-7*D*c)+b*(15*A*d^3-15*B*c*d^2+10*C*c^2*d-8*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^3/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2)/sqrt(-b*x^2+a),x,11,2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^2/(-a*d^2+b*c^2)/sqrt(d*x+c)-2/3*D*sqrt(d*x+c)*sqrt(-b*x^2+a)/b/d^2+2/3*sqrt(a)*(a*d^2*(3*C*d-5*D*c)-b*(3*A*d^3-3*B*c*d^2+6*C*c^2*d-8*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^3/(-a*d^2+b*c^2)/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-2/3*sqrt(a)*(a*d^2*D-b*(-3*B*d^2+6*C*c*d-8*D*c^2))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/b^(3/2)/d^3/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2)/sqrt(-b*x^2+a),x,11,2/3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^2/(-a*d^2+b*c^2)/(d*x+c)^(3/2)+2/3*(3*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(-4*A*d^3+B*c*d^2+2*C*c^2*d-5*D*c^3))*sqrt(-b*x^2+a)/d^2/(-a*d^2+b*c^2)^2/sqrt(d*x+c)-2/3*sqrt(a)*(3*a^2*d^4*D+3*a*b*d^2*(-B*d^2+2*C*c*d-5*D*c^2)-b^2*c*(-4*A*d^3+B*c*d^2+2*C*c^2*d-8*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^3/(-a*d^2+b*c^2)^2/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)+2/3*sqrt(a)*(3*a*d^2*(C*d-3*D*c)-b*(-A*d^3+B*c*d^2+2*C*c^2*d-8*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^3/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^(7/2)/sqrt(-b*x^2+a),x,12,2/5*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*sqrt(-b*x^2+a)/d^2/(-a*d^2+b*c^2)/(d*x+c)^(5/2)+2/15*(5*a*d^2*(-B*d^2+2*C*c*d-3*D*c^2)-b*c*(-8*A*d^3+3*B*c*d^2+2*C*c^2*d-7*D*c^3))*sqrt(-b*x^2+a)/d^2/(-a*d^2+b*c^2)^2/(d*x+c)^(3/2)+2/15*(15*a^2*d^4*(C*d-3*D*c)-b^2*c^2*(-23*A*d^3+3*B*c*d^2+2*C*c^2*d+8*D*c^3)+a*b*d^2*(9*A*d^3-29*B*c*d^2+19*C*c^2*d+21*D*c^3))*sqrt(-b*x^2+a)/d^2/(-a*d^2+b*c^2)^3/sqrt(d*x+c)-2/15*sqrt(a)*sqrt(b)*(15*a^2*d^4*(C*d-3*D*c)-b^2*c^2*(-23*A*d^3+3*B*c*d^2+2*C*c^2*d+8*D*c^3)+a*b*d^2*(9*A*d^3-29*B*c*d^2+19*C*c^2*d+21*D*c^3))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/d^3/(-a*d^2+b*c^2)^3/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-2/15*sqrt(a)*(15*a^2*d^4*D-5*a*b*d^2*(-B*d^2+2*C*c*d+3*D*c^2)+b^2*c*(-8*A*d^3+3*B*c*d^2+2*C*c^2*d+8*D*c^3))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(b)/d^3/(-a*d^2+b*c^2)^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(5/2)*(D*x^3+C*x^2+B*x+A)/(-b*x^2+a)^(3/2),x,13,(a*(B+a*D/b)+(A*b+C*a)*x)*(d*x+c)^(5/2)/a/b/sqrt(-b*x^2+a)+1/105*(105*A*b^2*c*d+a*(225*a*d^2*D+b*(175*B*d^2+217*C*c*d+30*D*c^2)))*sqrt(d*x+c)*sqrt(-b*x^2+a)/a/b^3+1/35*(35*A*b*d+49*C*a*d+10*D*a*c)*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/a/b^2+2/7*D*(d*x+c)^(5/2)*sqrt(-b*x^2+a)/b^2+1/105*(105*A*b*d*(3*a*d^2+b*c^2)+a*(9*a*d^2*(49*C*d+110*D*c)+b*c*(700*B*d^2+427*C*c*d+30*D*c^2)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(5/2)/d/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/105*(-a*d^2+b*c^2)*(105*A*b^2*c*d+a*(225*a*d^2*D+b*(175*B*d^2+217*C*c*d+30*D*c^2)))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(7/2)/d/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(3/2)*(D*x^3+C*x^2+B*x+A)/(-b*x^2+a)^(3/2),x,12,(a*(B+a*D/b)+(A*b+C*a)*x)*(d*x+c)^(3/2)/a/b/sqrt(-b*x^2+a)+1/15*(15*A*b*d+25*C*a*d+6*D*a*c)*sqrt(d*x+c)*sqrt(-b*x^2+a)/a/b^2+2/5*D*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/b^2+1/15*(15*A*b^2*c*d+a*(63*a*d^2*D+b*(45*B*d^2+55*C*c*d+6*D*c^2)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(5/2)/d/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/15*(-a*d^2+b*c^2)*(15*A*b*d+25*C*a*d+6*D*a*c)*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(5/2)/d/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)*(D*x^3+C*x^2+B*x+A)/(-b*x^2+a)^(3/2),x,11,(a*(B+a*D/b)+(A*b+C*a)*x)*sqrt(d*x+c)/a/b/sqrt(-b*x^2+a)+2/3*D*sqrt(d*x+c)*sqrt(-b*x^2+a)/b^2+1/3*(3*A*b*d+9*C*a*d+2*D*a*c)*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(3/2)/d/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/3*(3*A*b^2*c*d-a*(5*a*d^2*D-b*(-3*B*d^2+3*C*c*d+2*D*c^2)))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(5/2)/d/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/sqrt(d*x+c)/(-b*x^2+a)^(3/2),x,10,sqrt(d*x+c)*(a*(-A*b*d+B*b*c-C*a*d+D*a*c)+b*(c*(A*b+C*a)-a*d*(B+a*D/b))*x)/a/b/(-a*d^2+b*c^2)/sqrt(-b*x^2+a)+(A*b*c*d+a*(c*C*d+2*c^2*D-d^2*(B*b+3*D*a)/b))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/sqrt(b)/d/(-a*d^2+b*c^2)/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-(A*b*d-C*a*d+2*D*a*c)*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(3/2)/d/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2)/(-b*x^2+a)^(3/2),x,11,(a*(-A*b*d+B*b*c-C*a*d+D*a*c)+b*(c*(A*b+C*a)-a*d*(B+a*D/b))*x)/a/b/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a)-(A*b*d*(3*a*d^2+b*c^2)+a*(a*d^2*(C*d-2*D*c)+b*c*(-4*B*d^2+3*C*c*d-2*D*c^2)))*sqrt(-b*x^2+a)/a/b/(-a*d^2+b*c^2)^2/sqrt(d*x+c)+(A*b*d*(3*a*d^2+b*c^2)+a*(a*d^2*(C*d-2*D*c)+b*c*(-4*B*d^2+3*C*c*d-2*D*c^2)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/sqrt(b)/d/(-a*d^2+b*c^2)^2/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-(A*b^2*c*d+a*(a*d^2*D+b*(-B*d^2+C*c*d-2*D*c^2)))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/b^(3/2)/d/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2)/(-b*x^2+a)^(3/2),x,12,(a*(-A*b*d+B*b*c-C*a*d+D*a*c)+b*(c*(A*b+C*a)-a*d*(B+a*D/b))*x)/a/b/(-a*d^2+b*c^2)/(d*x+c)^(3/2)/sqrt(-b*x^2+a)-1/3*(A*b*d*(5*a*d^2+3*b*c^2)+a*(3*a*d^2*(C*d-2*D*c)+b*c*(-8*B*d^2+5*C*c*d-2*D*c^2)))*sqrt(-b*x^2+a)/a/b/(-a*d^2+b*c^2)^2/(d*x+c)^(3/2)-1/3*(A*b^2*c*d*(29*a*d^2+3*b*c^2)-a*(3*a^2*d^4*D-3*a*b*d^2*(-3*B*d^2+7*C*c*d-9*D*c^2)-b^2*c^2*(-23*B*d^2+11*C*c*d-2*D*c^2)))*sqrt(-b*x^2+a)/a/b/(-a*d^2+b*c^2)^3/sqrt(d*x+c)+1/3*(A*b^2*c*d*(29*a*d^2+3*b*c^2)-a*(3*a^2*d^4*D-3*a*b*d^2*(-3*B*d^2+7*C*c*d-9*D*c^2)-b^2*c^2*(-23*B*d^2+11*C*c*d-2*D*c^2)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/sqrt(b)/d/(-a*d^2+b*c^2)^3/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/3*(A*b*d*(5*a*d^2+3*b*c^2)+a*(3*a*d^2*(C*d-2*D*c)+b*c*(-8*B*d^2+5*C*c*d-2*D*c^2)))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/sqrt(a)/sqrt(b)/d/(-a*d^2+b*c^2)^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(7/2)*(D*x^3+C*x^2+B*x+A)/(-b*x^2+a)^(5/2),x,13,1/3*(a*(B+a*D/b)+(A*b+C*a)*x)*(d*x+c)^(7/2)/a/b/(-b*x^2+a)^(3/2)-1/6*(d*x+c)^(5/2)*(3*a*(A*b*d+3*C*a*d+2*D*a*c)-(4*A*b^2*c-a*(7*B*b*d+2*C*b*c+13*D*a*d))*x)/a^2/b^2/sqrt(-b*x^2+a)+1/30*d*(5*A*b*(-5*a*d^2+4*b*c^2)-a*(5*b*c*(7*B*d+2*C*c)+3*a*d*(25*C*d+49*D*c)))*sqrt(d*x+c)*sqrt(-b*x^2+a)/a^2/b^3+1/30*d*(20*A*b^2*c-35*B*a*b*d-10*C*a*b*c-77*D*a^2*d)*(d*x+c)^(3/2)*sqrt(-b*x^2+a)/a^2/b^3+1/30*(20*A*b^2*c*(-2*a*d^2+b*c^2)-a*(5*b^2*c^2*(7*B*d+2*C*c)+231*a^2*d^3*D+3*a*b*d*(35*B*d^2+110*C*c*d+119*D*c^2)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(7/2)/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/30*(-a*d^2+b*c^2)*(5*A*b*(-5*a*d^2+4*b*c^2)-a*(5*b*c*(7*B*d+2*C*c)+3*a*d*(25*C*d+49*D*c)))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(7/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(5/2)*(D*x^3+C*x^2+B*x+A)/(-b*x^2+a)^(5/2),x,12,1/3*(a*(B+a*D/b)+(A*b+C*a)*x)*(d*x+c)^(5/2)/a/b/(-b*x^2+a)^(3/2)-1/6*(d*x+c)^(3/2)*(a*(A*b*d+7*C*a*d+6*D*a*c)-(4*A*b^2*c-a*(5*B*b*d+2*C*b*c+11*D*a*d))*x)/a^2/b^2/sqrt(-b*x^2+a)+1/6*d*(4*A*b^2*c-a*(5*B*b*d+2*C*b*c+15*D*a*d))*sqrt(d*x+c)*sqrt(-b*x^2+a)/a^2/b^3+1/6*(A*b*(-3*a*d^2+4*b*c^2)-a*(b*c*(5*B*d+2*C*c)+3*a*d*(7*C*d+15*D*c)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(5/2)/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/6*(-a*d^2+b*c^2)*(4*A*b^2*c-a*(5*B*b*d+2*C*b*c+15*D*a*d))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(7/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^(3/2)*(D*x^3+C*x^2+B*x+A)/(-b*x^2+a)^(5/2),x,11,1/3*(a*(B+a*D/b)+(A*b+C*a)*x)*(d*x+c)^(3/2)/a/b/(-b*x^2+a)^(3/2)+1/6*sqrt(d*x+c)*(a*(A*b*d-5*C*a*d-6*D*a*c)+(4*A*b^2*c-a*(3*B*b*d+2*C*b*c+9*D*a*d))*x)/a^2/b^2/sqrt(-b*x^2+a)+1/6*(4*A*b^2*c-a*(3*B*b*d+2*C*b*c+21*D*a*d))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(5/2)/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/6*(A*b*(-a*d^2+4*b*c^2)-a*(b*c*(3*B*d+2*C*c)-a*d*(5*C*d-3*D*c)))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(5/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[sqrt(d*x+c)*(D*x^3+C*x^2+B*x+A)/(-b*x^2+a)^(5/2),x,11,1/3*(a*(B+a*D/b)+(A*b+C*a)*x)*sqrt(d*x+c)/a/b/(-b*x^2+a)^(3/2)-1/6*sqrt(d*x+c)*(a*(A*b^2*c*d-a*(7*a*d^2*D-b*(-B*d^2+C*c*d+6*D*c^2)))-b*(A*b*(-3*a*d^2+4*b*c^2)-a*(b*c*(B*d+2*C*c)-a*d*(3*C*d-D*c)))*x)/a^2/b^2/(-a*d^2+b*c^2)/sqrt(-b*x^2+a)+1/6*(A*b*(-3*a*d^2+4*b*c^2)-a*(b*c*(B*d+2*C*c)-a*d*(3*C*d-D*c)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(3/2)/(-a*d^2+b*c^2)/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/6*(4*A*b^2*c-a*(b*(B*d+2*C*c)-5*a*d*D))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(5/2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/sqrt(d*x+c)/(-b*x^2+a)^(5/2),x,11,1/3*sqrt(d*x+c)*(a*(-A*b*d+B*b*c-C*a*d+D*a*c)+b*(c*(A*b+C*a)-a*d*(B+a*D/b))*x)/a/b/(-a*d^2+b*c^2)/(-b*x^2+a)^(3/2)-1/6*sqrt(d*x+c)*(a*(A*b*d*(-5*a*d^2+b*c^2)+a*(a*d^2*(C*d-2*D*c)-b*c*(-4*B*d^2+5*C*c*d-6*D*c^2)))-(4*A*b^2*c*(-2*a*d^2+b*c^2)-a*(b^2*c^2*(-B*d+2*C*c)+3*a^2*d^3*D+a*b*d*(-3*B*d^2+2*C*c*d-7*D*c^2)))*x)/a^2/b/(-a*d^2+b*c^2)^2/sqrt(-b*x^2+a)+1/6*(4*A*b^2*c*(-2*a*d^2+b*c^2)-a*(b^2*c^2*(-B*d+2*C*c)+3*a^2*d^3*D+a*b*d*(-3*B*d^2+2*C*c*d-7*D*c^2)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(3/2)/(-a*d^2+b*c^2)^2/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/6*(A*b*(-5*a*d^2+4*b*c^2)-a*(b*c*(-B*d+2*C*c)-a*d*(C*d+D*c)))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(3/2)/(-a*d^2+b*c^2)/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2)/(-b*x^2+a)^(5/2),x,12,1/3*(a*(-A*b*d+B*b*c-C*a*d+D*a*c)+b*(c*(A*b+C*a)-a*d*(B+a*D/b))*x)/a/b/(-a*d^2+b*c^2)/sqrt(d*x+c)/(-b*x^2+a)^(3/2)+1/6*(a*(A*b*d*(7*a*d^2+b*c^2)+a*(a*d^2*(C*d-2*D*c)+b*c*(-8*B*d^2+7*C*c*d-6*D*c^2)))+(4*A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(-3*B*d+2*C*c)+a^2*d^3*D+a*b*d*(-5*B*d^2+6*C*c*d-9*D*c^2)))*x)/a^2/b/(-a*d^2+b*c^2)^2/sqrt(d*x+c)/sqrt(-b*x^2+a)-1/6*d*(A*b*(-21*a^2*d^4-15*a*b*c^2*d^2+4*b^2*c^4)-a*(b^2*c^3*(-3*B*d+2*C*c)+a^2*d^3*(3*C*d-5*D*c)+a*b*c*d*(-29*B*d^2+27*C*c*d-27*D*c^2)))*sqrt(-b*x^2+a)/a^2/b/(-a*d^2+b*c^2)^3/sqrt(d*x+c)+1/6*(A*b*(-21*a^2*d^4-15*a*b*c^2*d^2+4*b^2*c^4)-a*(b^2*c^3*(-3*B*d+2*C*c)+a^2*d^3*(3*C*d-5*D*c)+a*b*c*d*(-29*B*d^2+27*C*c*d-27*D*c^2)))*sqrt(d*x+c)*sqrt((-b*x^2+a)/a)*EllipticE(sin(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2))),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/sqrt(b)/(-a*d^2+b*c^2)^3/sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))/sqrt(-b*x^2+a)-1/6*(4*A*b^2*c*(-3*a*d^2+b*c^2)-a*(b^2*c^2*(-3*B*d+2*C*c)+a^2*d^3*D+a*b*d*(-5*B*d^2+6*C*c*d-9*D*c^2)))*sqrt((d*x+c)/(c+sqrt(a)*d/sqrt(b)))*sqrt((-b*x^2+a)/a)*InverseJacobiAM(arcsin(sqrt(1-sqrt(b)*x/sqrt(a))/sqrt(2)),sqrt(2*sqrt(a)*d/(sqrt(b)*c+sqrt(a)*d)))/a^(3/2)/b^(3/2)/(-a*d^2+b*c^2)^2/sqrt(d*x+c)/sqrt(-b*x^2+a),1],
[(d*x+c)^n*sqrt(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x,5,(C*d*(5+n)-c*D*(8+n))*(d*x+c)^(1+n)*(b*x^2+a)^(3/2)/b/d^2/(4+n)/(5+n)+D*(d*x+c)^(2+n)*(b*x^2+a)^(3/2)/b/d^2/(5+n)-(a*d^2*(1+n)*(C*d*(5+n)-c*D*(8+n))+b*(12*c^3*D-3*c^2*C*d*(5+n)+B*c*d^2*(n^2+9*n+20)-A*d^3*(n^2+9*n+20)))*(d*x+c)^(1+n)*sqrt(b*x^2+a)*AppellF1(1+n,-1/2,-1/2,2+n,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/b/d^4/(1+n)/(4+n)/(5+n)/sqrt(1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))/sqrt(1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))-(a*d^2*D*(n^2+6*n+8)-b*(12*c^2*D-3*c*C*d*(5+n)+B*d^2*(n^2+9*n+20)))*(d*x+c)^(2+n)*sqrt(b*x^2+a)*AppellF1(2+n,-1/2,-1/2,3+n,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/b/d^4/(2+n)/(4+n)/(5+n)/sqrt(1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))/sqrt(1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b))),1],
[(d*x+c)^n*(b*x^2+a)^p*(D*x^3+C*x^2+B*x+A),x,5,(C*d*(4+n+2*p)-c*D*(6+n+4*p))*(d*x+c)^(1+n)*(b*x^2+a)^(p+1)/b/d^2/(3+n+2*p)/(4+n+2*p)+D*(d*x+c)^(2+n)*(b*x^2+a)^(p+1)/b/d^2/(4+n+2*p)-(a*(1+n)*(C*d*(4+n+2*p)-c*D*(6+n+4*p))-b*(2*c^2*C*d*(p+1)*(4+n+2*p)-2*c^3*D*(2*p^2+5*p+3)-B*c*d^2*(n^2+4*n*p+4*p^2+7*n+14*p+12)+A*d^3*(n^2+4*n*p+4*p^2+7*n+14*p+12))/d^2)*(d*x+c)^(1+n)*(b*x^2+a)^p*AppellF1(1+n,-p,-p,2+n,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/b/d^2/(1+n)/(3+n+2*p)/(4+n+2*p)/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p)-(a*d^2*D*(2+n)*(3+n+2*p)+b*(2*c*C*d*(p+1)*(4+n+2*p)-2*c^2*D*(2*p^2+5*p+3)-B*d^2*(n^2+4*n*p+4*p^2+7*n+14*p+12)))*(d*x+c)^(2+n)*(b*x^2+a)^p*AppellF1(2+n,-p,-p,3+n,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/b/d^4/(2+n)/(3+n+2*p)/(4+n+2*p)/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p),1],
[(d*x+c)^(-3-2*p)*(b*x^2+a)^p*(D*x^3+C*x^2+B*x+A),x,5,D*(d*x+c)^(-1-2*p)*(b*x^2+a)^(p+1)/b/d^2-1/2*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*(b*x^2+a)^(p+1)/d^2/(a*d^2+b*c^2)/(p+1)/((d*x+c)^(2*p+2))-1/2*(C*d-c*D*(3+2*p))*(b*x^2+a)^p*AppellF1(-2*p,-p,-p,1-2*p,(d*x+c)/(c-sqrt(-a)*d/sqrt(b)),(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))/d^4/p/((d*x+c)^(2*p))/((1-(d*x+c)/(c-sqrt(-a)*d/sqrt(b)))^p)/((1-(d*x+c)/(c+sqrt(-a)*d/sqrt(b)))^p)-(a^2*d^4*D*(1+2*p)-b^2*(c^3*C*d-A*c*d^3-c^4*D*(3+2*p))-a*b*d^2*(2*c*C*d-B*d^2-c^2*D*(5+4*p)))*(sqrt(-a)-sqrt(b)*x)*(d*x+c)^(-1-2*p)*(b*x^2+a)^p*hypergeom([-1-2*p, -p],[-2*p],2*sqrt(-a)*sqrt(b)*(d*x+c)/(sqrt(b)*c-sqrt(-a)*d)/(sqrt(-a)-sqrt(b)*x))/b/d^3/(sqrt(b)*c+sqrt(-a)*d)/(a*d^2+b*c^2)/(1+2*p)/((-(sqrt(b)*c+sqrt(-a)*d)*(sqrt(-a)+sqrt(b)*x)/(sqrt(b)*c-sqrt(-a)*d)/(sqrt(-a)-sqrt(b)*x))^p),1]]: